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Plowhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/culinary-herbs/images/img068.webpProphecy of Many Toothsome Disheshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/culinary-herbs/images/img072.webpAnise in Flower and in Fruithttps://openoldbooks.sgp1.digitaloceanspaces.com/books/culinary-herbs/images/img078.webpSweet Basilhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/culinary-herbs/images/img082.webpBorage, Famous for Cool Tankardhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/culinary-herbs/images/img086.webpCaraway for Comfits and Birthday Cakeshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/culinary-herbs/images/img090.webpCatnip, Pussy's Delighthttps://openoldbooks.sgp1.digitaloceanspaces.com/books/culinary-herbs/images/img094.webpCoriander, for Old-Fashioned Candieshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/culinary-herbs/images/img098.webpDill, of Pickle Famehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/culinary-herbs/images/img102.webpSweet Fennelhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/culinary-herbs/images/img114.webpSweet Marjoramhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/culinary-herbs/images/img118.webpMint, Best Friend of Roast Lambhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/culinary-herbs/images/img122.webpCurled Parsleyhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/culinary-herbs/images/img136.webpRue, Sour Herb of Gracehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/culinary-herbs/images/img138.webpSage, the Leading Herb for Duck and Goose Dressinghttps://openoldbooks.sgp1.digitaloceanspaces.com/books/culinary-herbs/images/img141.webpRelative Sizes of Holt's Mammoth and Common Sage Leaveshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/culinary-herbs/images/img142.webpDainty Summer Savoryhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/culinary-herbs/images/img147.webpTarragon, the French Chef's Delighthttps://openoldbooks.sgp1.digitaloceanspaces.com/books/culinary-herbs/images/img149.webpThyme for Sausagehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/culinary-herbs/images/img004.webpHerbs and Children, a Happy Harmonyhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/culinary-herbs/images/img013.webpSpading Forkhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/culinary-herbs/images/img014.webpBarrel Culture of Herbshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/culinary-herbs/images/img017.webpTransplanting Board and Dibblehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/culinary-herbs/images/img025.webpPopular Spadeshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/culinary-herbs/images/img028.webpLath Screen for Shading Bedshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/culinary-herbs/images/img030.webpHarvesting Thyme Grown on a Commercial Scalehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/culinary-herbs/images/img032.webpGarden Hoes of Various Styleshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/culinary-herbs/images/img034.webpDried Herbs in Paper and Tinhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/culinary-herbs/images/img036.webpHerb Solution Bottlehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/culinary-herbs/images/img038.webpPaper Sacks of Dried Herbs for Home Usehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/culinary-herbs/images/img039.webpHand Cultivator and Scarifier https://openoldbooks.com/books/cully/read2026-11-15T15:48:14.649Zmonthly0.6 https://openoldbooks.com/books/culm-rock/read2026-11-15T15:48:14.649Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/culm-rock/images/imgc.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/culm-rock/images/fig004.webpglyph 4https://openoldbooks.sgp1.digitaloceanspaces.com/books/culm-rock/images/fig005.webpglyph 5https://openoldbooks.sgp1.digitaloceanspaces.com/books/culm-rock/images/imgr.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/culm-rock/images/fig007.webpglyph 7https://openoldbooks.sgp1.digitaloceanspaces.com/books/culm-rock/images/imgt.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/culm-rock/images/fig009.webpglyph 9https://openoldbooks.sgp1.digitaloceanspaces.com/books/culm-rock/images/imgi.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/culm-rock/images/fig011.webpglyph 11https://openoldbooks.sgp1.digitaloceanspaces.com/books/culm-rock/images/fig012.webpglyph 12https://openoldbooks.sgp1.digitaloceanspaces.com/books/culm-rock/images/fig014.webpglyph 14https://openoldbooks.sgp1.digitaloceanspaces.com/books/culm-rock/images/fig015.webpglyph 15https://openoldbooks.sgp1.digitaloceanspaces.com/books/culm-rock/images/imgw.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/culm-rock/images/richardgrey.webpGood morning, Uncle Richardhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/culm-rock/images/fig017.webpglyph 17https://openoldbooks.sgp1.digitaloceanspaces.com/books/culm-rock/images/fig018.webpglyph 18https://openoldbooks.sgp1.digitaloceanspaces.com/books/culm-rock/images/fig020.webpglyph 20https://openoldbooks.sgp1.digitaloceanspaces.com/books/culm-rock/images/imgn.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/culm-rock/images/fig022.webpglyph 22https://openoldbooks.sgp1.digitaloceanspaces.com/books/culm-rock/images/imga.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/culm-rock/images/hagargrey.webpDis yer is brofhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/culm-rock/images/fig031.webpglyph 31https://openoldbooks.sgp1.digitaloceanspaces.com/books/culm-rock/images/imgd.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/culm-rock/images/fig036.webpglyph 36https://openoldbooks.sgp1.digitaloceanspaces.com/books/culm-rock/images/imgy.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/culm-rock/images/imgs.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/culm-rock/images/rockgrey.webpCulm Rockhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/culm-rock/images/imgh.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/culm-rock/images/itsigrey.webpIt's I, Uncle Richard https://openoldbooks.com/books/cultural-exchange/read2026-11-15T15:48:14.649Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/cultural-exchange/images/illus.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cultural-exchange/images/cover.webp https://openoldbooks.com/books/cultural-exchange-61263/read2026-11-15T15:48:14.649Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/cultural-exchange-61263/images/illus.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cultural-exchange-61263/images/cover.webp https://openoldbooks.com/books/culture-and-anarchy/read2026-11-15T15:48:14.649Zmonthly0.6 https://openoldbooks.com/books/culture-and-cooking/read2026-11-15T15:48:14.649Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/culture-and-cooking/images/cover2.webp https://openoldbooks.com/books/culture-ethnology/read2026-11-15T15:48:14.649Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/culture-ethnology/images/cover.webpcover image not available https://openoldbooks.com/books/culture-s-garland/read2026-11-15T15:48:14.649Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/culture-s-garland/images/i_xv.webpA simple black-and-white ink illustration depicting a circular necklace or string made of thirteen sausages, with two additional matching links hanging straight down from the bottom center closure.https://openoldbooks.sgp1.digitaloceanspaces.com/books/culture-s-garland/images/i_005.webpJudge Thomas M. Cooleyhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/culture-s-garland/images/i_008.webpJudge Cooleyhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/culture-s-garland/images/i_022.webpA black-and-white ink illustration of an open, upturned human right hand, shown from the wrist up. The palm lines are prominently detailed and labeled with small letters "A", "B", "C", "D", and "E". The wrist features a gathered shirt cuff with a distinct, square cufflink.https://openoldbooks.sgp1.digitaloceanspaces.com/books/culture-s-garland/images/i_056.webpA satirical black-and-white ink illustration of a coat of arms. The central shield is split vertically down the middle; the left side features a pillow with a small ant, while the right side is divided into four horizontal blank bars. Flanking the shield as supporters are two Black men in caricature style, dressed in railway porter attire. A flowing banner arches over the top of the shield carrying the Latin motto "PRO PATRIA CAVALIERE".https://openoldbooks.sgp1.digitaloceanspaces.com/books/culture-s-garland/images/i_061.webp’roundThree line drawings of legs showing different styles of historical hosiery: on the left, a loose, wrinkled stocking held below the knee by a simple garter band; in the middle, a front-facing leg wearing a mesh-patterned stocking secured by a buttoned strap below the knee; and on the right, a solid black stocking held up by a garter suspender.https://openoldbooks.sgp1.digitaloceanspaces.com/books/culture-s-garland/images/i_183.webpA satirical, hand-lettered performance schedule titled "GRAND ITALIAN OPERA. FIRST WEEK." It lists the days from Monday through Saturday, substituting the names of the operas and the featured singers (preceded by "Mme." or "Mlle.") with small drawings of hazelnuts. The text below reads: "Assisted by a superb company of [hazelnuts] and an able corps de ballet including all the most noted terpsichorean [hazelnuts] of the century."https://openoldbooks.sgp1.digitaloceanspaces.com/books/culture-s-garland/images/i_259_1.webpA top-down line diagram of a rectangular pool table showing six pockets, a cue ball with an arrow indicating its trajectory, and a triangular rack of fifteen object balls. Solid black lines map out complex geometric angles and bounce paths across the table cushions.https://openoldbooks.sgp1.digitaloceanspaces.com/books/culture-s-garland/images/i_259_2.webpA top-down line diagram of a vertical pool table layout. An arrow points to a cue ball moving toward the upper left corner pocket, while a curved line tracks a ball flying completely off the top-right edge of the table, striking one of the spectators full in the nose.https://openoldbooks.sgp1.digitaloceanspaces.com/books/culture-s-garland/images/i_260.webpA top-down line diagram of a rectangular pool table with six pockets. On the left side of the table, a pool cue strikes a cue ball, creating a small, messy impact scribble. From the hit, a wavy, curved line traces the erratic path of the ball across the green, ending at a small, solid black circle.https://openoldbooks.sgp1.digitaloceanspaces.com/books/culture-s-garland/images/i_326.webpA simple black-and-white line drawing of a wooden gallows structure. It consists of a horizontal crossbeam supported by two vertical side posts with diagonal corner braces. A rope hangs from the center of the crossbeam, terminating in a noose, with the rest of the rope trailing down toward the right post.https://openoldbooks.sgp1.digitaloceanspaces.com/books/culture-s-garland/images/i_033.webpA high-contrast, black-and-white ink illustration showing the lower half of an actor. The figure wears dark, heavily silhouetted breeches or baggy trousers tucked into shoes, while the upper portion features a distinct, vertically striped pattern .https://openoldbooks.sgp1.digitaloceanspaces.com/books/culture-s-garland/images/i_034_1.webpA high-contrast black silhouette of a personhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/culture-s-garland/images/i_034_2.webpA high-contrast black silhouette showing the lower body and legs of a figure facing left.https://openoldbooks.sgp1.digitaloceanspaces.com/books/culture-s-garland/images/i_034_3.webpA black-and-white ink illustration focusing on a pair of legs from the thighs down.https://openoldbooks.sgp1.digitaloceanspaces.com/books/culture-s-garland/images/i_035_1.webpA high-contrast black silhouette of a pair of legs from the upper thighs down. The legs are extended downward in a slight V-shape, with the left foot pointing outward to the left and the right foot angled slightly downward.https://openoldbooks.sgp1.digitaloceanspaces.com/books/culture-s-garland/images/i_035_2.webpA high-contrast black silhouette showing a pair of legs standing slightly apart.https://openoldbooks.sgp1.digitaloceanspaces.com/books/culture-s-garland/images/i_036_1.webpA high-contrast black silhouette of a pair of legs.https://openoldbooks.sgp1.digitaloceanspaces.com/books/culture-s-garland/images/i_036_2.webpA high-contrast ink illustration showing a lower body and legs from the waist down in profile, facing left.https://openoldbooks.sgp1.digitaloceanspaces.com/books/culture-s-garland/images/i_037.webpA high-contrast black-and-white ink illustration of a pair of legs.https://openoldbooks.sgp1.digitaloceanspaces.com/books/culture-s-garland/images/i000.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/culture-s-garland/images/i_title.webpAn ornate shield emblem featuring the stylized, intertwined monogram letters "T & Co" or "T and C" at the center, framed by decorative scrollwork, with a rolled scroll or document suspended by a cord at the top.https://openoldbooks.sgp1.digitaloceanspaces.com/books/culture-s-garland/images/i_043_1.webpWilliam Shakespearehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/culture-s-garland/images/i_043_2.webpSir Francis Baconhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/culture-s-garland/images/i_044.webpBen Jonsonhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/culture-s-garland/images/i_045.webpFrancis Beaumonthttps://openoldbooks.sgp1.digitaloceanspaces.com/books/culture-s-garland/images/i_046.webpJohn Fletcherhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/culture-s-garland/images/i_047.webpRobert Greenehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/culture-s-garland/images/i_048.webpGeorge Peelehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/culture-s-garland/images/i_165.webpA black-and-white ink illustration of a bearded man in profile facing left, dressed in a short, pleated classical Greek tunic with a geometric Greek key pattern along the hem. https://openoldbooks.com/books/cultus-arborum/read2026-11-15T15:48:14.649Zmonthly0.6 https://openoldbooks.com/books/cum-grano-salis/read2026-11-15T15:48:14.649Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/cum-grano-salis/images/img-61.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cum-grano-salis/images/img-68.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cum-grano-salis/images/img-75.webp https://openoldbooks.com/books/cumberland-island/read2026-11-15T15:48:14.649Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/cumberland-island/images/p01.webpJUNIOR RANGERhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cumberland-island/images/p03.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cumberland-island/images/p03d.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cumberland-island/images/p03e.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cumberland-island/images/p03f.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cumberland-island/images/p03g.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cumberland-island/images/p03h.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cumberland-island/images/turtle2.webpJunior says:https://openoldbooks.sgp1.digitaloceanspaces.com/books/cumberland-island/images/p05b1.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cumberland-island/images/p05b2.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cumberland-island/images/p05b3.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cumberland-island/images/p05b4.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cumberland-island/images/p05c1.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cumberland-island/images/p05c2.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cumberland-island/images/p05c3.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cumberland-island/images/p05c4.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cumberland-island/images/turtle3.webpJunior says:https://openoldbooks.sgp1.digitaloceanspaces.com/books/cumberland-island/images/cover.webpJunior Ranger Program: Cumberland Island National Seashorehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cumberland-island/images/turtle1.webpJuniorhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cumberland-island/images/p02.webpForest habitathttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cumberland-island/images/p02a3.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cumberland-island/images/p02a4.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cumberland-island/images/p02a5.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cumberland-island/images/p02a6.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cumberland-island/images/p02a7.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cumberland-island/images/qe1.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cumberland-island/images/qe2.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cumberland-island/images/qe3.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cumberland-island/images/qe4.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cumberland-island/images/p05.webpDraw the dotshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cumberland-island/images/qa1.webpShell fragmenthttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cumberland-island/images/qb1.webpShellhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cumberland-island/images/qa2.webpShell fragmenthttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cumberland-island/images/qb2.webpShellhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cumberland-island/images/qa3.webpShell fragmenthttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cumberland-island/images/qb3.webpShellhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cumberland-island/images/qa4.webpShell fragmenthttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cumberland-island/images/qb4.webpShellhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cumberland-island/images/turtle4.webpJunior says:https://openoldbooks.sgp1.digitaloceanspaces.com/books/cumberland-island/images/p07c.webpNATIONAL PARK SERVICEhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cumberland-island/images/p07d.webpNational Park Service logo outlinehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cumberland-island/images/p08.webpCertificate of Stewardship https://openoldbooks.com/books/cuming-s-tour-to-the-western-country-1807-1809/read2026-11-15T15:48:14.649Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/cuming-s-tour-to-the-western-country-1807-1809/images/i-decor.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cuming-s-tour-to-the-western-country-1807-1809/images/i-original-title.webp https://openoldbooks.com/books/cumner-s-son-and-other-south-sea-folk/read2026-11-15T15:48:14.649Zmonthly0.6 https://openoldbooks.com/books/cumner-s-son-and-other-south-sea-folk-volume-01/read2026-11-15T15:48:14.649Zmonthly0.6 https://openoldbooks.com/books/cumner-s-son-and-other-south-sea-folk-volume-02/read2026-11-15T15:48:14.649Zmonthly0.6 https://openoldbooks.com/books/cumner-s-son-and-other-south-sea-folk-volume-03/read2026-11-15T15:48:14.649Zmonthly0.6 https://openoldbooks.com/books/cumner-s-son-and-other-south-sea-folk-volume-04/read2026-11-15T15:48:14.649Zmonthly0.6 https://openoldbooks.com/books/cumner-s-son-and-other-south-sea-folk-volume-05/read2026-11-15T15:48:14.649Zmonthly0.6 https://openoldbooks.com/books/cumulative-book-review-digest-v-1-1905/read2026-11-15T15:48:14.649Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/cumulative-book-review-digest-v-1-1905/images/full0001.webpTHE CUMULATIVE BOOK REVIEW DIGEST EVALUATION OF LITERATURE https://openoldbooks.com/books/cunnie-rabbit-mr-spider-and-the-other-beef/read2026-11-15T15:48:14.649Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/cunnie-rabbit-mr-spider-and-the-other-beef/images/dropcap-t.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cunnie-rabbit-mr-spider-and-the-other-beef/images/image37.webpThe Devil's Magic Eggs.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cunnie-rabbit-mr-spider-and-the-other-beef/images/image38.webpToothache.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cunnie-rabbit-mr-spider-and-the-other-beef/images/image39.webpWhy Mr. Spider's waist is small.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cunnie-rabbit-mr-spider-and-the-other-beef/images/image3.webp"Spider takes the hammer soffle." [See p. 43, line 3.]https://openoldbooks.sgp1.digitaloceanspaces.com/books/cunnie-rabbit-mr-spider-and-the-other-beef/images/dropcap-w.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cunnie-rabbit-mr-spider-and-the-other-beef/images/image4.webpThe Deer after fighting with Goro. [See p. 56.]https://openoldbooks.sgp1.digitaloceanspaces.com/books/cunnie-rabbit-mr-spider-and-the-other-beef/images/image5.webpThe Elephant after the fight with the Goro.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cunnie-rabbit-mr-spider-and-the-other-beef/images/image6.webpDe Conk.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cunnie-rabbit-mr-spider-and-the-other-beef/images/image7.webpMr. Spider sells a very fine dog.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cunnie-rabbit-mr-spider-and-the-other-beef/images/image8.webpMr. Turtle makes a riding-horse of Mr. Leopard.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cunnie-rabbit-mr-spider-and-the-other-beef/images/dropcap-s.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cunnie-rabbit-mr-spider-and-the-other-beef/images/image9.webpCunning Rabbit and his well.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cunnie-rabbit-mr-spider-and-the-other-beef/images/image10.webpMr. Spider pretends to die.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cunnie-rabbit-mr-spider-and-the-other-beef/images/image11.webp"De Country-fashion Man look de groun'."https://openoldbooks.sgp1.digitaloceanspaces.com/books/cunnie-rabbit-mr-spider-and-the-other-beef/images/image12.webpThe Wax Girl.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cunnie-rabbit-mr-spider-and-the-other-beef/images/image13.webpMr. Chameleon transformed into a boat.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cunnie-rabbit-mr-spider-and-the-other-beef/images/image14.webpMr. Spider challenges Pawpawtámus.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cunnie-rabbit-mr-spider-and-the-other-beef/images/dropcap-a.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cunnie-rabbit-mr-spider-and-the-other-beef/images/image15.webpThe Purro Devil.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cunnie-rabbit-mr-spider-and-the-other-beef/images/image16.webpCunnie Rabbit pretends to blow all the horns.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cunnie-rabbit-mr-spider-and-the-other-beef/images/image17.webp"One tem fowl bin gadder all togedder."https://openoldbooks.sgp1.digitaloceanspaces.com/books/cunnie-rabbit-mr-spider-and-the-other-beef/images/image18.webpThe Black Monkey starts after Mr. Spider.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cunnie-rabbit-mr-spider-and-the-other-beef/images/image19.webp"De pot begin fo' run f'om Spider."https://openoldbooks.sgp1.digitaloceanspaces.com/books/cunnie-rabbit-mr-spider-and-the-other-beef/images/image20.webpThe Devil turns Pigeon.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cunnie-rabbit-mr-spider-and-the-other-beef/images/dropcap-o.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cunnie-rabbit-mr-spider-and-the-other-beef/images/image44.webpThe End.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cunnie-rabbit-mr-spider-and-the-other-beef/images/cover-image.webpCover for Cunnie Rabbit, Mr. Spider and the other beefhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cunnie-rabbit-mr-spider-and-the-other-beef/images/image1.webpA GHOST STORY. [See Chap. XI.]https://openoldbooks.sgp1.digitaloceanspaces.com/books/cunnie-rabbit-mr-spider-and-the-other-beef/images/image2.webpTitle pagehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cunnie-rabbit-mr-spider-and-the-other-beef/images/image42.webpWatch-Pot and Greedy.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cunnie-rabbit-mr-spider-and-the-other-beef/images/image43.webpThe Origin of the Axe.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cunnie-rabbit-mr-spider-and-the-other-beef/images/dropcap-i.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cunnie-rabbit-mr-spider-and-the-other-beef/images/image33.webpThe Dancing Bird.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cunnie-rabbit-mr-spider-and-the-other-beef/images/image34.webpThe Wicked is taken in his own Snare.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cunnie-rabbit-mr-spider-and-the-other-beef/images/image35.webpAn Old Man turns Elephant.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cunnie-rabbit-mr-spider-and-the-other-beef/images/image36.webpThe Man who could not keep Secrets.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cunnie-rabbit-mr-spider-and-the-other-beef/images/image40.webpMr. Spider secures a powerful Witch Medicine.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cunnie-rabbit-mr-spider-and-the-other-beef/images/image41.webpMr. Spider gets into Trouble again.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cunnie-rabbit-mr-spider-and-the-other-beef/images/image21.webpThe Stone with the Beard.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cunnie-rabbit-mr-spider-and-the-other-beef/images/image22.webp"De debble, he duh sleep close the road-side."https://openoldbooks.sgp1.digitaloceanspaces.com/books/cunnie-rabbit-mr-spider-and-the-other-beef/images/image23.webpMarry the Devil, the Devil to pay.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cunnie-rabbit-mr-spider-and-the-other-beef/images/dropcap-n.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cunnie-rabbit-mr-spider-and-the-other-beef/images/image24.webpThe Three Twins.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cunnie-rabbit-mr-spider-and-the-other-beef/images/image25.webpWhich twin restored his father to life?https://openoldbooks.sgp1.digitaloceanspaces.com/books/cunnie-rabbit-mr-spider-and-the-other-beef/images/image26.webpTuckmahfongkah fals down the well.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cunnie-rabbit-mr-spider-and-the-other-beef/images/image27.webpMr. Spider creates a frightful tornadohttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cunnie-rabbit-mr-spider-and-the-other-beef/images/image28.webpMr. Leopard shows his hand.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cunnie-rabbit-mr-spider-and-the-other-beef/images/image29.webpMr. Leopard fools the other animals.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cunnie-rabbit-mr-spider-and-the-other-beef/images/image30.webpA case of Tit for Tat.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cunnie-rabbit-mr-spider-and-the-other-beef/images/image31.webpDr. Spider's fatal prescriptions.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cunnie-rabbit-mr-spider-and-the-other-beef/images/image32.webpMr. Spider "pulls" a supply of beef. https://openoldbooks.com/books/cuore-heart/read2026-11-15T15:48:14.649Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/cuore-heart/images/charcoal.webpTHE CHARCOAL MAN AND THE GENTLEMAN.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cuore-heart/images/rascals.webp“STOP THAT, YOU LITTLE RASCALS!”https://openoldbooks.sgp1.digitaloceanspaces.com/books/cuore-heart/images/resin.webp“THE BOYS HAD DAUBED THEIR HANDS WITH RESIN.”https://openoldbooks.sgp1.digitaloceanspaces.com/books/cuore-heart/images/cover.webpCuore, Edmondo de Amicishttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cuore-heart/images/title.webpA Book for Boyshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cuore-heart/images/troop.webp“THEN THE TROOP DARTED OUT OF THE DOOR.”https://openoldbooks.sgp1.digitaloceanspaces.com/books/cuore-heart/images/boy.webp“THE BOY HAD WALKED TEN MILES.”https://openoldbooks.sgp1.digitaloceanspaces.com/books/cuore-heart/images/deputy.webp“HURRAH FOR THE DEPUTY OF CALABRIA!”https://openoldbooks.sgp1.digitaloceanspaces.com/books/cuore-heart/images/marco.webp“HE STOOD WATCHING THE CONVOY UNTIL IT WAS LOST TO SIGHT.”https://openoldbooks.sgp1.digitaloceanspaces.com/books/cuore-heart/images/street.webp“WE DESCENDED, RUNNING AND SINGING.” https://openoldbooks.com/books/cup-bearers-of-wine-and-hellebore/read2026-11-15T15:48:14.649Zmonthly0.6 https://openoldbooks.com/books/cupid-and-the-law/read2026-11-15T15:48:14.649Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-and-the-law/images/drop_t.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-and-the-law/images/drop_b.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-and-the-law/images/drop_o.webp https://openoldbooks.com/books/cupid-in-africa/read2026-11-15T15:48:14.649Zmonthly0.6 https://openoldbooks.com/books/cupid-of-campion/read2026-11-15T15:48:14.649Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-of-campion/images/cover.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-of-campion/images/titlep.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-of-campion/images/logo.webp https://openoldbooks.com/books/cupid-s-almanac/read2026-11-15T15:48:14.649Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-almanac/images/illus-0007-5.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-almanac/images/illus-0007-6.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-almanac/images/illus-0007-7.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-almanac/images/illus-0008-1.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-almanac/images/illus-0008-2.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-almanac/images/illus-0009-1.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-almanac/images/illus-engagements2.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-almanac/images/illus-0010-1.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-almanac/images/illus-0016-1.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-almanac/images/illus-0017-1.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-almanac/images/illus-0018-1.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-almanac/images/illus-0020-1.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-almanac/images/illus-0021-1.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-almanac/images/illus-notes-on-exp-work.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-almanac/images/illus-0022-1.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-almanac/images/illus-0024-1.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-almanac/images/illus-0025-1.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-almanac/images/illus-0026-1.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-almanac/images/illus-0028-1.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-almanac/images/illus-0029-1.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-almanac/images/illus-0030-1.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-almanac/images/illus-0032-1.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-almanac/images/illus-0033-1.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-almanac/images/illus-0034-1.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-almanac/images/illus-0040-1.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-almanac/images/illus-0041-1.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-almanac/images/illus-0042-1.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-almanac/images/illus-0044-1.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-almanac/images/illus-0045-1.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-almanac/images/img046.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-almanac/images/illus-0048-1.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-almanac/images/illus-0049-1.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-almanac/images/illus-0050-1.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-almanac/images/illus-0052-1.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-almanac/images/illus-0053-1.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-almanac/images/illus-0054-1.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-almanac/images/illus-0056-1.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-almanac/images/illus-0057-1.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-almanac/images/illus-0002-1.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-almanac/images/illus-0004-1.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-almanac/images/illus-0003-1.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-almanac/images/illus-0005-1.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-almanac/images/illus-0006-1.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-almanac/images/illus-0007-1.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-almanac/images/illus-0007-2.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-almanac/images/illus-0007-3.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-almanac/images/illus-0007-4.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-almanac/images/illus-0008-3.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-almanac/images/illus-0012-1.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-almanac/images/illus-0013-1.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-almanac/images/illus-0014-1.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-almanac/images/illus-0036-1.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-almanac/images/illus-0037-1.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-almanac/images/illus-0038-1.webp https://openoldbooks.com/books/cupid-s-cyclopedia/read2026-11-15T15:48:14.649Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-cyclopedia/images/dropcap-a.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-cyclopedia/images/illus-a.webpA, as described in this passagehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-cyclopedia/images/arms.webpA coat of arms, motto FORGET ME NOThttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-cyclopedia/images/cupid3.webpCupid in an easy-chair, smoking a pipehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-cyclopedia/images/fp1.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-cyclopedia/images/dropcap-b.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-cyclopedia/images/illus-b.webpB, as described in this passagehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-cyclopedia/images/dropcap-d.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-cyclopedia/images/illus-d.webpD, as described in this passagehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-cyclopedia/images/fp2.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-cyclopedia/images/dropcap-f.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-cyclopedia/images/illus-f.webpF, as described in this passagehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-cyclopedia/images/fig1.webpA fig leafhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-cyclopedia/images/dropcap-g.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-cyclopedia/images/illus-g.webpG, as described in this passagehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-cyclopedia/images/fp3.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-cyclopedia/images/dropcap-j.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-cyclopedia/images/illus-j.webpJ, as described in this passagehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-cyclopedia/images/cupid4.webpCupid reading a book titled WISDOMhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-cyclopedia/images/dropcap-m.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-cyclopedia/images/illus-m.webpM, as described in this passagehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-cyclopedia/images/fp5.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-cyclopedia/images/dropcap-n.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-cyclopedia/images/illus-n.webpN, as described in this passagehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-cyclopedia/images/dropcap-o.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-cyclopedia/images/illus-o.webpO, as described in this passagehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-cyclopedia/images/cupid5.webpCupid, seated on a rock by a flower, reading a paperhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-cyclopedia/images/dropcap-r.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-cyclopedia/images/illus-r.webpR, as described in this passagehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-cyclopedia/images/dropcap-s.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-cyclopedia/images/illus-s.webpS, as described in this passagehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-cyclopedia/images/dropcap-v.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-cyclopedia/images/illus-v.webpV, as described in this passagehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-cyclopedia/images/dropcap-w.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-cyclopedia/images/w-hand.webpSymbol as describedhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-cyclopedia/images/illus-w.webpW, as described in this passagehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-cyclopedia/images/cupid6.webpCupid sitting against a stack of bookshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-cyclopedia/images/fp8.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-cyclopedia/images/dropcap-z.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-cyclopedia/images/illus-z.webpZ, as described in this passagehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-cyclopedia/images/z-symbol-1.webpZ-shaped symbolhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-cyclopedia/images/z-symbol-2.webpZ-shaped symbolhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-cyclopedia/images/map.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-cyclopedia/images/cover.webpCover imagehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-cyclopedia/images/cupid1.webpCupidhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-cyclopedia/images/frontispiece.webpFrontispiece: Cupid surrounded by clouds and flowershttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-cyclopedia/images/cupid-titlepage.webpCupidhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-cyclopedia/images/copyright.webpPicture of a bee gazing at a honey jar; the label forms the copyright noticehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-cyclopedia/images/cupid2.webpCupidhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-cyclopedia/images/signature.webp(signatures)https://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-cyclopedia/images/dropcap-c.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-cyclopedia/images/illus-c.webpC, as described in this passagehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-cyclopedia/images/dropcap-e.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-cyclopedia/images/illus-e.webpE, as described in this passagehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-cyclopedia/images/dropcap-h.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-cyclopedia/images/illus-h.webpH, as described in this 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hearthttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-cyclopedia/images/fp9.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-cyclopedia/images/dropcap-y.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-cyclopedia/images/illus-y.webpY, as described in this passage https://openoldbooks.com/books/cupid-s-fair-weather-booke/read2026-11-15T15:48:14.649Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-fair-weather-booke/images/month-01-illus1.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-fair-weather-booke/images/month-01-illus2.webpA water bottlehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-fair-weather-booke/images/month-01-illus3.webpA Pledge rosettehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-fair-weather-booke/images/month-01-illus4.webpBust of a lady in a sailor-suit-style collar, above 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pipehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-fair-weather-booke/images/frontispiece.webpFrontispiecehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-fair-weather-booke/images/titlepage.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-fair-weather-booke/images/copyright.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-fair-weather-booke/images/heart.webpA red hearthttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-fair-weather-booke/images/signature.webp(signatures)https://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-fair-weather-booke/images/cupid2.webpA cupid reading a bookhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-fair-weather-booke/images/month-02-illus1.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-fair-weather-booke/images/month-02-illus2.webpSaint Valentine, 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https://openoldbooks.com/books/cupid-s-middleman/read2026-11-15T15:48:14.649Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-middleman/images/gs04.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-middleman/images/gs03.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-middleman/images/gs05.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-middleman/images/gs02.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-middleman/images/cover01.webpCover.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cupid-s-middleman/images/gs01.webp https://openoldbooks.com/books/cupid-s-understudy/read2026-11-15T15:48:14.649Zmonthly0.6 https://openoldbooks.com/books/cupology/read2026-11-15T15:48:14.649Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/cupology/images/cup01.webp[Illustration: cup01]https://openoldbooks.sgp1.digitaloceanspaces.com/books/cupology/images/cup02.webp[Illustration: cup02]https://openoldbooks.sgp1.digitaloceanspaces.com/books/cupology/images/cup03.webp[Illustration: cup03]https://openoldbooks.sgp1.digitaloceanspaces.com/books/cupology/images/cup04.webp[Illustration: cup04]https://openoldbooks.sgp1.digitaloceanspaces.com/books/cupology/images/cup05.webp[Illustration: cup05]https://openoldbooks.sgp1.digitaloceanspaces.com/books/cupology/images/cup06.webp[Illustration: cup06]https://openoldbooks.sgp1.digitaloceanspaces.com/books/cupology/images/cup07.webp[Illustration: cup07] https://openoldbooks.com/books/cups-and-their-customs/read2026-11-15T15:48:14.649Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/cups-and-their-customs/images/frontis.webpSprigs in a glass cuphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cups-and-their-customs/images/works.webpworkshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cups-and-their-customs/images/natural.webpNatural History of the British Isles https://openoldbooks.com/books/curialia-miscellanea-or-anecdotes-of-old-times-regal-noble-gentilitial-and-misce/read2026-11-15T15:48:14.649Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/curialia-miscellanea-or-anecdotes-of-old-times-regal-noble-gentilitial-and-misce/images/church.webpchurchhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curialia-miscellanea-or-anecdotes-of-old-times-regal-noble-gentilitial-and-misce/images/rectory.webprectoryhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curialia-miscellanea-or-anecdotes-of-old-times-regal-noble-gentilitial-and-misce/images/revolution.webpRevolutionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curialia-miscellanea-or-anecdotes-of-old-times-regal-noble-gentilitial-and-misce/images/title.webptitle pagehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curialia-miscellanea-or-anecdotes-of-old-times-regal-noble-gentilitial-and-misce/images/frontispiece.webpPegge https://openoldbooks.com/books/curiosa-mathematica-part-2-pillow-problems/read2026-11-15T15:48:14.649Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/cover.webpThis book offers 72 math puzzles solved mentally during sleepless nights, covering arithmetic, algebra, and geometry.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1.svgelement of opening downwardshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/2.svgsegmenthttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/3.svgsinehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/4.svgcosinehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/5.svgplushttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/6.svgminushttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/i_f007.webpA simple geometric diagram of a semicircle with labeled points — P on the arc, O at the center, and N on the diameter — illustrating a classical geometry or trigonometry problem.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/7.svgupper O upper Phttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/8.svgupper P upper Nhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/9.svgupper N upper O upper Phttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/10.svgupper O upper Nhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/11.svgsinehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/12.svgcosinehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/13.svgsemicirclehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/14.svghttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/15.svghttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/16.svghttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/17.svgb squared plus c squared minus a squaredhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/18.svg2 plus 3 greater than 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upper B cosine upper C period EndRoothttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/153.svgcotangent upper B upper A upper D equals StartFraction left parenthesis m plus n right parenthesis cotangent upper A plus n cotangent upper B Over m EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/154.svgcotangent upper C upper A upper D equals StartFraction left parenthesis m plus n right parenthesis cotangent upper A plus m cotangent upper C Over n EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/155.svgStartFraction 8.2 Superscript one fourth Baseline period left parenthesis StartRoot 2 EndRoot plus 1 right parenthesis Over 3 EndFraction periodhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/156.svgStartFraction 2 Superscript m Baseline period left parenthesis alpha minus beta right parenthesis plus beta Over 2 Superscript m Baseline period left parenthesis alpha minus beta right parenthesis plus 2 beta EndFraction periodhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/157.svgupper Xhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/158.svgupper Yhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/159.svgupper Zhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/160.svghttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/161.svgStartLayout 1st Row 1st Column left parenthesis x plus StartRoot 3 EndRoot period y right parenthesis period left parenthesis h minus z right parenthesis 2nd Column equals a h semicolon 2nd Row 1st Column x squared plus y squared 2nd Column equals a squared period EndLayouthttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/162.svgk equals StartFraction theta minus upper B Over upper A EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/163.svgl equals StartFraction theta minus upper C Over upper B EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/164.svgm equals StartFraction theta minus upper A Over upper C EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/165.svgStartFraction a prime Over a EndFraction equals StartFraction b prime Over b EndFraction equals StartFraction c prime Over c EndFraction equals 2 cosine theta periodhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/166.svg18 dot 65 degreehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/167.svg14 dot 53 degreehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/168.svghttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/169.svgu squared plus v squared equals 2https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/170.svgleft parenthesis 1 plus k right parenthesis comma left parenthesis 1 minus k right parenthesishttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/171.svg2 m squaredhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/172.svgm squaredhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/173.svgStartFraction u squared Over m squared EndFraction plus StartFraction v squared Over m squared EndFraction equals 2https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/174.svgleft parenthesis m squared plus k right parenthesis comma left parenthesis m squared minus k right parenthesishttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/175.svgleft single quotation mark left parenthesis a squared plus b squared plus 2 a b right parenthesis comma left parenthesis a squared plus b squared minus 2 a b right parenthesis right single quotation markhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/176.svgleft parenthesis a squared plus b squared right parenthesishttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/177.svg2 a bhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/178.svgStartLayout 1st Row StartLayout 1st Row 1st Column a 2nd Column equals x squared minus y squared comma 2nd Row 1st Column b 2nd Column equals 2 x y semicolon 3rd Row 1st Column therefore a squared plus b squared 2nd Column equals left parenthesis x squared plus y squared right parenthesis squared semicolon EndLayout 2nd Row therefore the formula left single quotation mark u squared plus v squared equals 2 m squared right single quotation mark becomes 3rd Row left parenthesis x squared minus y squared plus 2 x y right parenthesis squared plus left parenthesis x squared minus y squared minus 2 x y right parenthesis squared equals 2 left parenthesis x squared plus y squared right parenthesis squared semicolon 4th Row i period e period left parenthesis StartFraction x squared minus y squared plus 2 x y Over x squared plus y squared EndFraction right parenthesis squared plus left parenthesis StartFraction x squared minus y squared minus 2 x y Over x squared plus y squared EndFraction right parenthesis squared equals 2 period EndLayouthttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/i_p029.webpA geometric diagram of triangle ABC with multiple lines radiating from base point F to vertices and interior points A', B', C', D, E.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/179.svgupper D upper Ehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/180.svgupper B upper D plus upper C upper E equals upper B upper Chttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/181.svgupper C upper F equals upper C upper Ehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/182.svgupper D upper Fhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/183.svgupper E upper Fhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/184.svgangle upper B upper D upper F equals angle upper B upper F upper D equals left bracket by upper I period 29 right bracket angle upper F upper D upper Ehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/185.svgangle upper C upper E upper F equals angle upper F upper E upper Dhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/186.svgtherefore angle s upper B upper D upper E comma upper C upper E upper Dhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/187.svgupper Fhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/188.svgcircled dothttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/189.svgwhite up pointing triangle upper A upper D upper Ehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/190.svgperpendicularhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/191.svgupper A upper Fhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/192.svgangle upper Ahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/193.svgupper F upper B primehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/194.svgupper F upper C primehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/195.svgperpendicular upper A upper Chttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/196.svgupper F upper A prime perpendicular upper B upper Chttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/197.svgupper A primehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/198.svgupper D upper E perpendicular upper F upper A primehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/199.svgparallel to upper B upper Chttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/200.svgbecause anglehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/201.svgupper B primehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/202.svgupper C primehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/203.svgupper F upper A Superscript prime Baseline equals upper F upper B Superscript prime Baseline equals upper F upper C primehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/204.svgtherefore anglehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/205.svgupper B upper D upper Ehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/206.svgupper C upper E upper Dhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/207.svgangle upper B upper F upper D equals angle upper F upper D upper A primehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/208.svgthereforehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/209.svgequals angle upper B upper D upper Fhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/210.svgtherefore upper B upper F equals upper B upper Dhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/211.svgtherefore upper B upper C equals upper B upper D plus upper C upper Ehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/i_p030a.webpA geometric diagram of quadrilateral ABCD with interior points E, F, G, H forming an inscribed quadrilateral, connected by crossing diagonals.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/212.svgupper A upper B upper C upper Dhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/213.svgupper C upper Dhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/214.svgupper E upper F upper G upper Hhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/215.svgbecausehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/216.svgupper B upper C upper Dhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/217.svgtherefore upper F upper Ghttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/218.svgupper E upper Hhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/219.svgupper F upper Ghttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/220.svgtherefore upper E upper Hhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/221.svgupper A upper E upper Hhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/222.svgupper A upper Ehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/223.svgtherefore upper A upper Hhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/i_p030b.webpA geometric diagram of triangle ABC with an inscribed triangle A'B'C' and central point O, connected by multiple cevians.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/224.svgangle upper B upper A prime upper C Superscript prime Baseline equals angle upper C upper A prime upper B primehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/225.svgupper A prime upper C primehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/226.svgupper A prime upper B primehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/227.svgperpendicular upper B upper Chttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/228.svgangle upper C prime upper A prime upper B primehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/229.svg2 alphahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/230.svgleft parenthesis beta plus gamma right parenthesis equals pi minus angle upper B prime upper O upper C Superscript prime Baseline equals upper Ahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/231.svgtherefore 2 upper A equals 2 left parenthesis beta plus gamma right parenthesis equals pi minus 2 alphahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/232.svgtherefore alpha equals 90 degree negative upper Ahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/233.svgtherefore angle upper B upper A prime upper C Superscript prime Baseline equals upper Ahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/234.svgangle upper B upper C prime upper A Superscript prime Baseline equals upper Chttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/235.svgupper B upper C prime upper A primehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/236.svgupper B upper C upper Ahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/237.svgStartLayout 1st Row 1st Column therefore upper B upper A prime 2nd Column equals StartFraction c Over a EndFraction dot upper B upper C Superscript prime Baseline equals StartFraction c Over a EndFraction dot left parenthesis c minus upper A upper C Superscript prime Baseline right parenthesis comma 2nd Row 1st Column Blank 2nd Column equals StartFraction c Over a EndFraction dot left parenthesis c minus StartFraction b Over c EndFraction dot upper A upper B Superscript prime Baseline right parenthesis comma 3rd Row 1st Column Blank 2nd Column equals StartFraction c squared Over a EndFraction minus StartFraction b Over a EndFraction dot left parenthesis b minus upper C upper B Superscript prime Baseline right parenthesis comma 4th Row 1st Column Blank 2nd Column equals StartFraction c squared Over a EndFraction minus StartFraction b squared Over a EndFraction plus StartFraction b Over a EndFraction dot StartFraction a Over b EndFraction dot upper C upper A Superscript prime Baseline comma 5th Row 1st Column Blank 2nd Column equals StartFraction c squared Over a EndFraction minus StartFraction b squared Over a EndFraction plus a minus upper B upper A Superscript prime Baseline semicolon 6th Row 1st Column therefore 2 upper B upper A prime 2nd Column equals StartFraction c squared plus a squared minus b squared Over a EndFraction equals StartFraction 2 c a cosine upper B Over a EndFraction semicolon 7th Row 1st Column therefore upper B upper A prime 2nd Column equals c cosine upper B semicolon EndLayouthttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/238.svgtherefore upper A primehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/239.svgone half dot 1https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/240.svgone half dot one halfhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/241.svgone fourthhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/242.svgtwo thirdshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/243.svgone thirdhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/i_p032.webpA triangle with vertices A (apex, top right), B (bottom left), and C (bottom right). Point D lies on base BC between B and C, with line segment AD drawn from apex A down to D.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/244.svgcosine upper A upper D upper B plus cosine upper A upper D upper C equals 0https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/245.svgStartLayout 1st Row 1st Column therefore 2nd Column StartFraction alpha squared plus a squared minus 4 c squared Over 2 alpha a EndFraction plus StartFraction alpha squared plus a squared minus 4 b squared Over 2 alpha a EndFraction equals 0 semicolon 2nd Row 1st Column therefore 2 alpha squared 2nd Column plus 2 a squared minus 4 b squared minus 4 c squared equals 0 semicolon 3rd Row 1st Column therefore alpha squared 2nd Column equals minus a squared plus 2 b squared plus 2 c squared period 4th Row 1st Column Similarly comma beta squared 2nd Column equals 2 a squared minus b squared plus 2 c squared semicolon 5th Row 1st Column gamma squared 2nd Column equals 2 a squared plus 2 b squared minus c squared period EndLayouthttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/246.svgStartLayout 1st Row 1st Column Blank 2nd Column 2 k minus l plus 2 m equals 0 comma 2nd Row 1st Column and 2nd Column 2 k plus 2 l minus m equals 0 semicolon 3rd Row 1st Column therefore 2nd Column 3 left parenthesis l minus m right parenthesis equals 0 semicolon i period e period l equals m semicolon 4th Row 1st Column therefore 2nd Column 2 k equals negative l equals negative m semicolon EndLayouthttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/247.svgk equals negative 1 comma l equals 2 comma m equals 2https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/248.svgStartLayout 1st Row 1st Column Blank 2nd Column therefore minus alpha squared plus 2 beta squared plus 2 gamma squared equals 9 a squared semicolon 2nd Row 1st Column Blank 2nd Column i period e period a squared equals StartFraction minus alpha squared plus 2 beta squared plus 2 gamma squared Over 9 EndFraction semicolon 3rd Row 1st Column Blank 2nd Column therefore upper B upper C left parenthesis which equals 2 a right parenthesis equals two thirds StartRoot minus alpha squared plus 2 beta squared plus 2 gamma squared EndRoot comma ampersand c period comma EndLayouthttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/249.svgStartLayout 1st Row 1st Column Also cosine upper A 2nd Column equals StartFraction b squared plus c squared minus a squared Over 2 b c EndFraction 2nd Row 1st Column Blank 2nd Column equals StartFraction 2 alpha squared minus beta squared plus 2 gamma squared plus 2 alpha squared plus 2 beta squared minus gamma squared plus alpha squared minus 2 beta squared minus 2 gamma squared Over 2 period StartRoot 2 alpha squared minus beta squared plus 2 gamma squared EndRoot period StartRoot 2 alpha squared plus 2 beta squared minus gamma squared EndRoot EndFraction 3rd Row 1st Column Blank 2nd Column equals StartFraction 5 alpha squared minus beta squared minus gamma squared Over den period EndFraction semicolon and so for other angles period EndLayouthttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/i_p033.webpA triangle with vertices A (bottom left), B (bottom right), and D (top right). Point C lies on side BD near D, and point E lies on the base outside the triangle to the right of B, with dashed lines from C and D down to E.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/250.svgStartLayout 1st Row 1st Column Now upper A upper E 2nd Column equals upper A upper D period secant upper A equals d secant upper A semicolon 2nd Row 1st Column therefore upper B upper E 2nd Column equals d secant upper A minus b period 3rd Row 1st Column Also upper B upper C 2nd Column equals upper B upper E period tangent upper E equals left parenthesis d secant upper A minus b right parenthesis period cotangent upper A comma 4th Row 1st Column Blank 2nd Column equals StartFraction d minus b cosine upper A Over sine upper A EndFraction semicolon EndLayouthttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/251.svgupper C upper D equals StartFraction b minus d cosine upper A Over sine upper A EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/i_p034.webpTriangle ABD with point C on side DB and external point E with dashed lines.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/252.svgStartLayout 1st Row 1st Column Also area 2nd Column equals one half dot left parenthesis upper A upper B period upper B upper C plus upper A upper D period upper D upper C right parenthesis comma 2nd Row 1st Column Blank 2nd Column equals one half dot StartFraction b period left parenthesis d minus b cosine upper A right parenthesis plus d period left parenthesis b minus d cosine upper A right parenthesis Over sine upper A EndFraction comma 3rd Row 1st Column Blank 2nd Column equals StartFraction 2 b d minus left parenthesis b squared plus d squared right parenthesis cosine upper A Over 2 sine upper A EndFraction semicolon which answers left parenthesis 2 right parenthesis period EndLayouthttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/253.svgm khttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/254.svgleft parenthesis m k plus m minus 1 right parenthesishttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/255.svgleft parenthesis m minus 2 right parenthesishttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/256.svgStartLayout 1st Row 1st Column m k plus m minus 1 2nd Column equals 4 left parenthesis m minus 2 right parenthesis comma 2nd Row 1st Column or else 4 left parenthesis m k plus m minus 1 right parenthesis 2nd Column equals m minus 2 period EndLayouthttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/257.svgm k equals 3 m minus 7https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/258.svgk equals 3 minus StartFraction 7 Over m EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/259.svgm equals 7https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/260.svgk equals 2https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/261.svg4 m k equals 2 minus 3 mhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/262.svgupper A upper Phttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/i_p035.webpParallelogram AEGF (left) and parallelogram AKPH (right) overlap near center points G, K, H, M. Line AC runs horizontally through base; line AB crosses diagonally upper right through point L and P, with interior intersection points labeled K, H, M.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/263.svgupper E upper A upper Fhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/264.svgperpendicular upper A upper Phttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/265.svgupper E upper Ghttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/266.svgupper F upper Hhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/267.svgupper G upper Hhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/268.svgupper K upper Ghttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/269.svgupper K upper Hhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/270.svgangle upper G upper K upper Hhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/271.svgupper P upper Lhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/272.svgupper P upper Mhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/273.svgupper A upper P upper Lhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/274.svgupper A upper K upper Ghttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/275.svgupper A upper Khttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/276.svgupper A upper P upper Mhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/277.svgupper A upper K upper Hhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/278.svgangle upper L upper P upper Mhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/279.svgx plus y plus z equals shttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/280.svgleft parenthesis y plus z right parenthesis comma left parenthesis z plus x right parenthesis comma left parenthesis x plus y right parenthesis semicolon i period e period it is StartFraction 2 s Over 3 EndFraction periodhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/281.svgone thirdhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/282.svgStartFraction s Over 3 EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/283.svgequals StartFraction 4 s Over 9 EndFraction plus StartFraction s Over 9 EndFraction equals StartFraction 5 s Over 9 EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/284.svgtherefore StartFraction 5 s Over 9 EndFraction equals 30 d period semicolon therefore s equals 54 d period equals 4 divided by 6 periodhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/i_p036.webpLarge triangle with vertices A (top), B (bottom left), and C (bottom right). Midpoints A' (on BC), B' (on AC), and C' (on AB) form an inscribed medial triangle A'B'C', with all six connecting segments drawn, creating four smaller congruent triangles inside.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/285.svgStartFraction upper B upper A Superscript prime Baseline Over upper A prime upper C Superscript prime Baseline EndFraction equals StartFraction sine left parenthesis upper B plus theta right parenthesis Over sine upper B EndFraction semicolon and StartFraction upper A prime upper C Over upper A prime upper B Superscript prime Baseline EndFraction equals StartFraction sine theta Over sine upper C EndFraction periodhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/286.svgtherefore upper B upper A equals StartFraction sine left parenthesis upper B plus theta right parenthesis Over sine upper B EndFraction period k a semicolon and upper A prime upper C equals StartFraction sine theta Over sine upper C EndFraction period k bhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/287.svgupper B upper A Superscript prime Baseline plus upper A prime upper C equals a semicolon therefore khttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/288.svgequals StartStartFraction a OverOver StartFraction a period sine left parenthesis upper B plus theta right parenthesis Over sine upper B EndFraction plus StartFraction b sine theta Over sine upper C EndFraction EndEndFraction equals StartStartFraction sine upper A OverOver StartFraction sine upper A sine left parenthesis upper B plus theta right parenthesis Over sine upper B EndFraction plus StartFraction sine upper B sine theta Over sine upper C EndFraction EndEndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/289.svgStartLayout 1st Row 1st Column equals 2nd Column StartFraction sine upper A sine upper B sine upper C Over sine upper A sine left parenthesis upper B plus theta right parenthesis sine upper C plus sine squared upper B sine theta EndFraction 2nd Row 1st Column equals 2nd Column StartFraction sine upper A sine upper B sine upper C Over sine upper A sine upper C left parenthesis sine upper B cosine theta plus cosine upper B sine theta right parenthesis plus left parenthesis 1 minus cosine squared upper B right parenthesis sine theta EndFraction 3rd Row 1st Column equals 2nd Column StartFraction sine upper A sine upper B sine upper C Over StartLayout 1st Row StartLayout 1st Row sine theta plus sine theta left parenthesis sine upper A sine upper C cosine upper B minus cosine squared upper B right parenthesis 2nd Row plus cosine theta sine upper A sine upper B sine upper C EndLayout EndLayout right brace EndFraction 4th Row 1st Column equals 2nd Column StartFraction sine upper A sine upper B sine upper C Over StartLayout 1st Row StartLayout 1st Row sine theta plus sine theta cosine upper B left parenthesis sine upper A sine upper C plus cosine left parenthesis upper A plus upper C right parenthesis right parenthesis 2nd Row plus cosine theta sine upper A sine upper B sine upper C EndLayout EndLayout right brace EndFraction 5th Row 1st Column equals 2nd Column StartFraction sine upper A sine upper B sine upper C Over sine theta left parenthesis 1 plus cosine upper A cosine upper B cosine upper C right parenthesis plus cosine theta sine upper A sine upper B sine upper C EndFraction period EndLayouthttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/290.svgk equals StartFraction sine upper A sine upper B sine upper C Over 1 plus cosine upper A cosine upper B cosine upper C EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/291.svgs equalshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/292.svgm equalshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/293.svgv equalshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/294.svgm equals StartRoot s period left parenthesis s minus a right parenthesis period left parenthesis s minus b right parenthesis period left parenthesis s minus c right parenthesis EndRoothttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/295.svgStartLayout 1st Row 1st Column therefore m squared 2nd Column equals s period left parenthesis s minus a right parenthesis period left parenthesis s minus b right parenthesis period left parenthesis s minus c right parenthesis semicolon 2nd Row 1st Column therefore StartFraction m squared Over s EndFraction 2nd Column equals s cubed minus s squared period left parenthesis a plus b plus c right parenthesis plus s period left parenthesis b c plus c a plus a b right parenthesis minus a b c semicolon 3rd Row 1st Column Blank 2nd Column equals s cubed minus 2 s cubed plus s period left parenthesis b c plus c a plus a b right parenthesis minus v semicolon 4th Row 1st Column therefore 2nd Column StartFraction m squared Over s squared EndFraction plus StartFraction v Over s EndFraction plus s squared equals b c plus c a plus a b semicolon 5th Row 1st Column therefore 2nd Column 2 period left parenthesis StartFraction m squared Over s squared EndFraction plus StartFraction v Over s EndFraction plus s squared right parenthesis equals left parenthesis a plus b plus c right parenthesis squared minus left parenthesis a squared plus b squared plus c squared right parenthesis semicolon 6th Row 1st Column Blank 2nd Column equals 4 s squared minus left parenthesis a squared plus b squared plus c squared right parenthesis semicolon 7th Row 1st Column therefore 2nd Column a squared plus b squared plus c squared equals 2 period left parenthesis s squared minus StartFraction v Over s EndFraction minus StartFraction m squared Over s squared EndFraction right parenthesis period EndLayouthttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/i_p038.webpA rhombus with vertices A (left), B (right), C (top), and D (bottom), with diagonals AB and CD intersecting at center. Points F and E lie on diagonal AB. An ellipse is inscribed touching all four sides, with tick marks at C and D indicating equal segments.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/296.svgupper C upper F upper D upper Ehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/297.svgupper C upper E equals b period tangent alphahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/298.svgupper C upper F equals a period tangent betahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/299.svgangle upper F upper C upper E equals angle upper A upper C upper E plus angle upper F upper C upper B minus gamma equals pi minus gammahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/300.svgtherefore sine upper F upper C upper E equals sine gammahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/301.svgupper F upper C upper E equals one half period a b period tangent alpha period tangent beta period sine gammahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/302.svgStartFraction a b sine alpha sine beta sine gamma Over cosine alpha cosine beta EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/303.svgupper Mhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/304.svgsine alpha equals StartFraction 2 upper M Over b c EndFraction comma sine beta equals StartFraction 2 upper M Over c a EndFraction comma sine gamma equals StartFraction 2 upper M Over a b EndFraction semicolonhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/305.svgStartLayout 1st Row 1st Column therefore area of Tetragon 2nd Column equals a b dot StartFraction 8 upper M cubed Over a squared b squared c squared EndFraction dot StartFraction 4 b c period c a Over left parenthesis b squared plus c squared minus a squared right parenthesis left parenthesis c squared plus a squared minus b squared right parenthesis EndFraction semicolon 2nd Row 1st Column Blank 2nd Column equals StartFraction 32 upper M cubed Over left parenthesis b squared plus c squared minus a squared right parenthesis period left parenthesis c squared plus a squared minus b squared right parenthesis EndFraction period EndLayouthttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/306.svgStartLayout 1st Row 1st Column Blank 2nd Column 3 left parenthesis a squared plus b squared plus c squared right parenthesis 2nd Row 1st Column Blank 2nd Column equals left parenthesis a plus b plus c right parenthesis squared plus left parenthesis b squared minus 2 b c plus c squared right parenthesis plus left parenthesis c squared minus 2 c a plus a squared right parenthesis plus left parenthesis a squared minus 2 a b plus b squared right parenthesis semicolon 3rd Row 1st Column Blank 2nd Column equals left parenthesis a plus b plus c right parenthesis squared plus left parenthesis b minus c right parenthesis squared plus left parenthesis c minus a right parenthesis squared plus left parenthesis a minus b right parenthesis squared period EndLayouthttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/307.svgStartLayout 1st Row 1st Column 3 left parenthesis 1 squared plus 2 squared plus 3 squared right parenthesis 2nd Column equals 6 squared plus 1 squared plus 2 squared plus 1 squared period 2nd Row 1st Column 3 left parenthesis 1 squared plus 3 squared plus 7 squared right parenthesis 2nd Column equals 11 squared plus 4 squared plus 6 squared plus 2 squared period EndLayouthttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/i_p039.webpRectangle ADCD with vertices A (top left), D (top right), C (bottom right), and B' (bottom, left of C). Point B lies on the base between B″ and B', with dashed lines from A to B″ (external left point) and solid cevians from A to B and B', forming overlapping triangles on a shared base.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/308.svgupper C upper Bhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/309.svgupper B primehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/310.svgupper B double primehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/311.svgupper A upper B primehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/312.svgupper A upper B double primehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/313.svgangle upper A upper B prime upper Chttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/314.svgangle upper A upper B double prime upper Chttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/315.svgangle upper A upper D upper Chttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/316.svgtherefore it equals angle upper A upper B upper Chttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/317.svgupper Whttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/318.svgupper W upper Whttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/319.svgupper W upper Bhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/320.svgone half dot two thirds plus one half dot one thirdhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/321.svgupper W upper W upper B upper Bhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/322.svgupper W upper B upper B upper Bhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/323.svgtwo thirds dot one half plus one third dot one fourthhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/i_p040.webpLarge triangle with vertices A (top), B (bottom left), C (bottom right). Segment DE is parallel to BC with D on AB and E on AC. Points F and G lie on BC, H on DE. Solid and dashed cevians cross between D, E, F, G, H, forming an inner quadrilateral with intersecting diagonals.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/324.svgupper E commahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/325.svgupper D upper F plus upper E upper G equals upper D upper Ehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/326.svgtherefore upper D upper B equals upper E upper Ghttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/327.svgupper E upper C equals upper D upper Fhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/328.svgtherefore upper D upper B plus upper E upper C equals upper D upper Ehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/329.svgupper B upper Hhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/330.svgupper C upper Hhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/331.svgtherefore angle upper D upper H upper B equals alternate angle upper H upper B upper F equals angle upper D upper B upper H semicolonhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/332.svgtherefore upper D upper B equals upper D upper H periodhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/333.svgupper E upper C equals upper E upper Hhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/334.svgtherefore upper D upper B plus upper E upper C equals upper D upper Ehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/335.svgtherefore upper E upper G equals upper D upper B comma and upper D upper F equals upper E upper C semicolonhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/336.svgtherefore upper D upper F plus upper E upper G equals upper D upper E periodhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/i_p041.webpLarge triangle with vertices A (top), B (bottom left), C (bottom right). Segment FG is parallel to BC with F on AB and G on AC. Points H, E, K lie on BC between B and C.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/337.svgupper F upper G perpendicularhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/338.svgupper G upper K perpendicular upper B upper Chttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/339.svgStartLayout 1st Row 1st Column Now upper F upper H must equals upper G upper K period 2nd Row 1st Column Also upper E upper F equals x sine upper B semicolon and upper F upper H 2nd Column equals upper E upper F sine upper F upper E upper H comma 3rd Row 1st Column Blank 2nd Column equals upper E upper F cosine upper B comma 4th Row 1st Column Blank 2nd Column equals x sine upper B cosine upper B semicolon 5th Row 1st Column similarly comma upper G upper K 2nd Column equals y sine upper C cosine upper C period EndLayouthttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/340.svgStartLayout 1st Row 1st Column But upper F upper H equals upper G upper K semicolon 2nd Column therefore x sine upper B cosine upper B equals y sine upper C cosine upper C semicolon 2nd Row 1st Column Blank 2nd Column therefore StartFraction x Over y EndFraction equals StartFraction sine 2 upper C Over sine 2 upper B EndFraction period EndLayouthttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/i_p042.webpA geometric figure with apex A (top), base vertices B (left), C (right), D (bottom), and midpoints F (upper left), G (upper right), E (center). Multiple triangulating segments connect all vertices, forming a faceted diamond-like shape with a small triangle marked at apex A.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/341.svgupper E upper G perpendicularhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/342.svgbecause upper B upper Dhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/343.svgupper F upper Ehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/344.svgperpendicular upper A upper B comma thereforehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/345.svgparallel tohttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/346.svgtherefore upper A upper F colon upper F upper B colon colon upper A upper E colon upper E upper Dhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/347.svgbecause upper C upper Dhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/348.svgupper G upper Ehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/349.svgperpendicular upper A upper C comma thereforehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/350.svgtherefore upper A upper G colon upper G upper C colon colon upper A upper E colon upper E upper Dhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/351.svgtherefore upper A upper F colon upper F upper B colon colon upper A upper G colon upper G upper Chttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/352.svgtherefore upper F upper Ghttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/353.svgupper A upper C upper Bhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/354.svgupper B upper A upper Chttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/355.svgupper C upper A upper Bhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/356.svgupper C upper B upper Ahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/357.svgone sixthhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/358.svgStartLayout 1st Row 1st Column for 2nd Column upper A upper B upper C comma one half times one third semicolon i period e period one sixth period 2nd Row 1st Column Blank 2nd Column upper A upper C upper B comma one half times one fourth semicolon i period e period one eighth period 3rd Row 1st Column Blank 2nd Column upper B upper A upper C comma two thirds times one half semicolon i period e period one third period 4th Row 1st Column Blank 2nd Column upper B upper C upper A comma two thirds times one fourth semicolon i period e period one sixth period 5th Row 1st Column Blank 2nd Column upper C upper A upper B comma three fourths times one half semicolon i period e period three eighths period 6th Row 1st Column Blank 2nd Column upper C upper B upper A comma three fourths times one third semicolon i period e period one fourth period EndLayouthttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/359.svgStartLayout 1st Row 1st Column Blank 2nd Column one thirty fourth dot left brace 4 times three fourths plus 3 times two thirds plus 8 times three fourths plus 4 times one half plus 9 times two thirds plus 6 times one half right brace semicolon 2nd Row 1st Column i period e period 2nd Column one thirty fourth times left brace 3 plus 2 plus 6 plus 2 plus 6 plus 3 right brace semicolon i period e period StartFraction 22 Over 34 EndFraction semicolon i period e period StartFraction 11 Over 17 EndFraction period EndLayouthttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/360.svgupper P upper Q perpendicular upper B upper Chttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/361.svgupper P upper R perpendicular upper A upper Bhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/362.svgupper P upper Q equals upper P upper Rhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/i_p043.webpTriangle ABC (lower, vertices B bottom-left, C bottom-right, A upper-middle) overlaps with triangle BEC (larger, apex E upper-right). Interior points R (on AB), D, P (on BC), and Q (on AC/AE) mark cevian intersections, with multiple segments drawn through A creating a dense central crossing.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/363.svgupper P upper C tangent upper C equals upper P upper B sine upper Bhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/364.svgtherefore upper P upper C colon upper P upper B colon colon sine upper B colon tangent upper Chttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/365.svgupper A upper D perpendicular upper B upper Chttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/366.svgStartLayout 1st Row colon colon StartFraction upper A upper D Over upper A upper B EndFraction colon StartFraction upper A upper D Over upper D upper C EndFraction comma 2nd Row colon colon upper D upper C colon upper A upper B period EndLayouthttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/367.svgupper A upper D perpendicular upper B upper Chttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/368.svgupper B upper Ahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/369.svgStartLayout 1st Row 1st Column Then StartFraction upper P upper Q Over upper P upper C EndFraction equals StartFraction upper A upper D Over upper D upper C EndFraction 2nd Column equals StartFraction upper A upper D Over upper A upper B EndFraction dot StartFraction upper A upper B Over upper D upper C EndFraction comma 2nd Row 1st Column Blank 2nd Column equals StartFraction upper P upper R Over upper P upper B EndFraction dot StartFraction upper A upper B Over upper A upper E EndFraction comma 3rd Row 1st Column Blank 2nd Column equals StartFraction upper P upper R Over upper P upper B EndFraction dot StartFraction upper P upper B Over upper P upper C EndFraction equals StartFraction upper P upper R Over upper P upper C EndFraction semicolon 4th Row 1st Column therefore upper P upper Q 2nd Column equals upper P upper R period EndLayouthttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/370.svgn period ModifyingAbove n plus 2 With quotation dash period ModifyingAbove n plus 4 With quotation dashhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/371.svgthereforehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/372.svgleft parenthesis n plus 1 right parenthesishttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/373.svgModifyingAbove n plus 1 With quotation dash period ModifyingAbove n plus 3 With quotation dash period ModifyingAbove n plus 5 With quotation dashhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/374.svgequals left parenthesis n plus 1 right parenthesis period left parenthesis ModifyingAbove n plus 2 With quotation dash plus 1 right parenthesis period left parenthesis n plus 5 right parenthesis semicolonhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/375.svgequals ModifyingAbove n plus 1 With quotation dash period ModifyingAbove n plus 2 With quotation dash period ModifyingAbove n plus 5 With quotation dash plus ModifyingAbove n plus 1 With quotation dash period ModifyingAbove n plus 5 With quotation dashhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/376.svgequals ModifyingAbove n plus 1 With quotation dash period ModifyingAbove n plus 2 With quotation dash period left parenthesis ModifyingAbove n plus 3 With quotation dash plus 2 right parenthesis plus ModifyingAbove n plus 1 With quotation dash period left parenthesis ModifyingAbove n plus 2 With quotation dash plus 3 right parenthesis semicolonhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/377.svgequals ModifyingAbove n plus 1 With quotation dash period ModifyingAbove n plus 2 With quotation dash period ModifyingAbove n plus 3 With quotation dash plus 2 period ModifyingAbove n plus 1 With quotation dash period ModifyingAbove n plus 2 With quotation dash plus ModifyingAbove n plus 1 With quotation dash period ModifyingAbove n plus 2 With quotation dash plus 3 period ModifyingAbove n plus 1 With quotation dash semicolonhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/378.svgequals ModifyingAbove n plus 1 With quotation dash period ModifyingAbove n plus 2 With quotation dash period ModifyingAbove n plus 3 With quotation dash plus 3 period ModifyingAbove n plus 1 With quotation dash period ModifyingAbove n plus 2 With quotation dash plus 3 period ModifyingAbove n plus 1 With quotation dash periodhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/379.svgtherefore upper S equals StartFraction n period ModifyingAbove n plus 1 With quotation dash period ModifyingAbove n plus 2 With quotation dash period ModifyingAbove n plus 3 With quotation dash Over 4 EndFraction plus n period ModifyingAbove n plus 1 With quotation dash period ModifyingAbove n plus 2 With quotation dash plus three halves period n period ModifyingAbove n plus 1 With quotation dash plus upper C semicolonhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/380.svgupper C equals 0 periodhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/381.svgtherefore upper S equals n period ModifyingAbove n plus 1 With quotation dash period left parenthesis StartFraction n squared plus 5 n plus 6 Over 4 EndFraction plus n plus 2 plus three halves right parenthesis semicolonhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/382.svgequals n period ModifyingAbove n plus 1 With quotation dash period StartFraction n squared plus 9 n plus 20 Over 4 EndFraction equals StartFraction n period ModifyingAbove n plus 1 With quotation dash period ModifyingAbove n plus 4 With quotation dash period ModifyingAbove n plus 5 With quotation dash Over 4 EndFraction periodhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/383.svgupper Shttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/384.svgequals StartFraction 100.101 .104 .105 Over 4 EndFraction equals 100.101 .26 .105 semicolonhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/385.svg101.105 equals 10 comma 605https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/386.svgtherefore 101.105 .13 equals 130 comma 000 plus 7800 plus 65 equals 137 comma 865https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/387.svgequals 274 comma 000 plus 1730 equals 275 comma 730https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/388.svgtherefore upper S equals 27 comma 573 comma 000https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/i_p045.webpA triangle with vertices A (top), B (bottom left), and C (bottom right). A vertical altitude is drawn from apex A perpendicular to base BC, with the altitude labeled α, dividing the base into two segments.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/389.svga alpha equals b beta equals c gammahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/390.svgtherefore alpha sine upper A equals beta sine upper B equals gamma sine upper Chttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/391.svgtherefore StartFraction sine upper A Over beta gamma EndFraction equals StartFraction sine upper B Over gamma alpha EndFraction equals StartFraction sine upper C Over alpha beta EndFraction equals khttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/392.svgtherefore sine upper A equals k beta gamma comma sine upper B equals k gamma alpha comma sine upper C equals k alpha betahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/393.svgsine left parenthesis upper A plus upper B right parenthesis equals sine upper Chttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/394.svgtherefore sine upper A cosine upper B plus cosine upper A sine upper B equals sine upper Chttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/395.svgtherefore sine upper A cosine upper B equals sine upper C minus cosine upper A sine upper Bhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/396.svgtherefore sine squared upper A left parenthesis 1 minus sine squared upper B right parenthesis equals sine squared upper C plus sine squared upper B left parenthesis 1 minus sine squared upper A right parenthesis minus 2 sine upper C cosine upper A sine upper Bhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/397.svgtherefore sine squared upper A minus sine squared upper A sine squared upper B equals sine squared upper C plus sine squared upper B minus sine squared upper A sine squared upper B minus 2 sine upper B sine upper C cosine upper Ahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/398.svgtherefore sine squared upper A minus sine squared upper B minus sine squared upper C equals minus 2 sine upper B sine upper C cosine upper Ahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/399.svgtherefore comma squaring comma left parenthesis sine Superscript 4 Baseline upper A plus ampersand c period right parenthesis minus 2 sine squared upper A sine squared upper B minus 2 sine squared upper A sine squared upper C plus 2 sine squared upper B sine squared upper C equals 4 sine squared upper B sine squared upper C left parenthesis 1 minus sine squared upper A right parenthesishttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/400.svgtherefore left parenthesis sine Superscript 4 Baseline upper A plus ampersand c period right parenthesis minus 2 left parenthesis sine squared upper B sine squared upper C plus ampersand c period right parenthesis plus 4 sine squared upper A sine squared upper B sine squared upper C equals 0https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/401.svgsine upper Ahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/402.svgk Superscript 4https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/403.svgleft parenthesis beta Superscript 4 Baseline gamma Superscript 4 Baseline plus ampersand c period right parenthesis minus 2 alpha squared beta squared gamma squared period left parenthesis alpha squared plus ampersand c period right parenthesis plus 4 k squared alpha Superscript 4 Baseline beta Superscript 4 Baseline gamma Superscript 4 Baseline equals 0https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/i_p046.webpTriangle ABC with altitude from A to base BC labeled α.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/404.svgtherefore k squared equals StartFraction 2 alpha squared beta squared gamma squared left parenthesis alpha squared plus ampersand c period right parenthesis minus left parenthesis beta Superscript 4 Baseline gamma Superscript 4 Baseline plus ampersand c period right parenthesis Over 4 alpha Superscript 4 Baseline beta Superscript 4 Baseline gamma Superscript 4 Baseline EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/405.svgsine upper A equals k beta gammahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/406.svgalpha equals b sine upper Chttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/407.svggamma equals a sine upper Bhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/408.svgtherefore a equals StartFraction gamma Over sine upper B EndFraction equals StartFraction gamma Over k gamma alpha EndFraction equals StartFraction 1 Over k alpha EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/409.svgequals StartFraction b c sine upper A Over 2 EndFraction equals one half dot StartFraction 1 Over k beta EndFraction dot StartFraction 1 Over k gamma EndFraction dot k beta gamma equals StartFraction 1 Over 2 k EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/410.svgStartLayout 1st Row 1st Column for 2nd Column 2 upper W 3rd Column one fourth semicolon 2nd Row 1st Column Blank 2nd Column 1 upper W comma 1 upper B 3rd Column one half semicolon 3rd Row 1st Column Blank 2nd Column 2 upper B 3rd Column one fourth period EndLayouthttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/411.svgStartLayout 1st Row 1st Column for 2nd Column 4 upper W comma 1 upper B 3rd Column one fourth semicolon 2nd Row 1st Column Blank 2nd Column 3 upper W comma 2 upper B 3rd Column one half semicolon 3rd Row 1st Column Blank 2nd Column 2 upper W comma 3 upper B 3rd Column one fourth period EndLayouthttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/412.svgthree fifthshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/413.svgthree tenthshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/414.svgthree twentiethshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/415.svgthree fortiethshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/416.svgtwo seventhshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/417.svgfour seventhshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/418.svgone seventhhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/419.svgStartLayout 1st Row 1st Column for 2nd Column 2 upper W 3rd Column two sevenths semicolon 2nd Row 1st Column Blank 2nd Column 1 upper W comma 1 upper B 3rd Column four sevenths semicolon 3rd Row 1st Column Blank 2nd Column 2 upper B 3rd Column one seventh period EndLayouthttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/420.svg1 upper Whttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/421.svgStartLayout 1st Row 1st Column for 2nd Column 3 upper W 3rd Column two sevenths semicolon 2nd Row 1st Column Blank 2nd Column 2 upper W comma 1 upper B 3rd Column four sevenths semicolon 3rd Row 1st Column Blank 2nd Column 1 upper W comma 2 upper B 3rd Column one seventh period EndLayouthttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/422.svg1 upper Whttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/423.svgeight twenty firstshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/424.svgone twenty firsthttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/425.svgsix fifteenthshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/426.svgeight fifteenthshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/427.svgone fifteenthhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/428.svgtwo fifthshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/i_p047.webpA triangle with vertices A (top), B (bottom left), C (bottom right). Three cevians AD, BE, and CF intersect at interior point O (centroid), where D lies on BC, E on AC, and F on AB, dividing the triangle into six smaller triangles meeting at O.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/429.svgStartLayout 1st Row 1st Column Because 2nd Column StartFraction upper D upper O Over upper O upper A EndFraction equals StartFraction white up pointing triangle upper D upper O upper C Over white up pointing triangle upper O upper A upper C EndFraction equals StartFraction white up pointing triangle upper D upper O upper B Over white up pointing triangle upper O upper A upper B EndFraction equals StartFraction white up pointing triangle upper O upper B upper C Over white up pointing triangle upper O upper C upper A plus white up pointing triangle upper O upper A upper B EndFraction semicolon 2nd Row 1st Column therefore 2nd Column StartFraction upper D upper O Over upper D upper A EndFraction equals StartFraction white up pointing triangle upper O upper B upper C Over white up pointing triangle upper A upper B upper C EndFraction period 3rd Row 1st Column Similarly comma 2nd Column StartFraction upper E upper O Over upper E upper B EndFraction equals StartFraction white up pointing triangle upper O upper C upper A Over white up pointing triangle upper A upper B upper C EndFraction comma and StartFraction upper F upper O Over upper F upper C EndFraction equals StartFraction white up pointing triangle upper O upper A upper B Over white up pointing triangle upper A upper B upper C EndFraction period 4th Row 1st Column Hence 2nd Column StartFraction upper D upper O Over upper D upper A EndFraction plus StartFraction upper E upper O Over upper E upper B EndFraction plus StartFraction upper F upper O Over upper F upper C EndFraction equals 1 period EndLayouthttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/430.svgupper Lhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/i_p048a.webpA horizontal line segment labeled ε (total length) above, subdivided into two portions: left part labeled (1−a) and right part labeled a, each marked with a brace beneath, showing a partition of the whole segment.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/431.svgupper E upper Ahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/i_p048b.webpA horizontal line segment with total length labeled (ε+a−1) above, subdivided into two portions: left part labeled (1−λ) and right part labeled λ, each marked with a brace beneath, showing a complementary partition of the whole segment.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/432.svgleft parenthesis epsilon minus ModifyingAbove 1 minus alpha With quotation dash right parenthesishttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/433.svgleft parenthesis epsilon plus alpha minus 1 right parenthesishttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/434.svgupper E upper A upper Lhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/435.svgleft parenthesis epsilon plus alpha minus 1 minus ModifyingAbove 1 minus lamda With quotation dash right parenthesishttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/436.svgleft parenthesis epsilon plus alpha plus lamda minus 2 right parenthesishttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/437.svgupper B prime upper C primehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/438.svgupper B upper B Superscript prime Baseline equals upper C upper C primehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/439.svgangle shttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/440.svgupper B prime upper B upper Chttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/441.svgupper C prime upper C upper Bhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/442.svgupper A prime upper A upper Chttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/443.svgupper C prime upper C upper Ahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/444.svgupper A prime upper A upper Bhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/445.svgupper B prime upper B upper Ahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/i_p049.webpA triangle with vertices A (top), B (bottom left), C (bottom right). Interior triangle A'B'C' is inscribed with A' (upper middle), B' (lower left), C' (lower right). Point D lies at the center of A'B'C', with cevians from each outer vertex through the inner triangle converging near D.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/446.svgangle upper B prime upper B upper Chttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/447.svgthetahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/448.svgangle upper C prime upper C upper B equals thetahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/449.svgtherefore angle upper C prime upper C upper A equals upper C minus theta equals angle upper A prime upper A upper Chttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/450.svgtherefore angle upper A prime upper A upper B equals upper A minus left parenthesis upper C minus theta right parenthesis equals angle upper B prime upper B upper Ahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/451.svgangle s upper B prime upper B upper C comma upper B prime upper B upper Ahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/452.svgequals upper Bhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/453.svgtherefore theta plus upper A minus left parenthesis upper C minus theta right parenthesis equals upper Bhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/454.svgtherefore 2 theta equals upper B plus upper C minus upper A equals 180 degree minus 2 upper Ahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/455.svgtherefore theta equals 90 degree negative upper Ahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/456.svgupper B upper B primehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/457.svgupper C upper C primehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/458.svgupper D upper B upper Chttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/459.svg2 upper Ahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/460.svgupper D upper B Superscript prime Baseline equals k period upper D upper Bhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/461.svgk period upper B upper Chttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/462.svgupper D upper Ahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/463.svgk period upper A upper Bhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/464.svgk period upper A upper Chttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/465.svgequals one half period left brace two thirds times one half plus one third times one half right brace equals one fourthhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/466.svgone half period left brace five sixths period one half plus one sixth period one half right brace equals one fourthhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/467.svgone half period left brace five sixths period one third plus one sixth period two thirds right brace equals seven thirty sixthshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/468.svgseven thirty sixthshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/469.svgStartFraction 9 comma 9 comma 7 Over 25 EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/470.svgfive sixthshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/471.svgfive sixths period nine twenty fifths equals three tenthshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/472.svgtwo thirds period nine twenty fifths equals six twenty fifthshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/473.svgone half period seven twenty fifths equals seven fiftiethshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/474.svgStartFraction 15 plus 12 plus 7 Over 50 EndFraction equals StartFraction 34 Over 50 EndFraction equals StartFraction 17 Over 25 EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/i_p050.webpA triangle with vertices A (top), B (bottom left), C (bottom right). Midpoints A' (on BC), B' (on AC), and C' (on AB) form inscribed medial triangle A'B'C'.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/475.svgupper B upper A Superscript prime Baseline equals xhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/476.svgx squared equals a period left parenthesis a minus x right parenthesishttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/477.svgx squared plus a x minus a squared equals 0https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/478.svgtherefore x equals StartFraction negative a plus or minus a StartRoot 5 EndRoot Over 2 EndFraction equals StartFraction a Over 2 EndFraction period left parenthesis StartRoot 5 EndRoot minus 1 right parenthesishttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/479.svgupper A upper B prime upper C primehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/480.svgStartLayout 1st Row 1st Column Blank 2nd Column equals one half period StartFraction c Over 2 EndFraction period left parenthesis StartRoot 5 EndRoot minus 1 right parenthesis period left brace b minus StartFraction b Over 2 EndFraction period left parenthesis StartRoot 5 EndRoot minus 1 right parenthesis right brace period sine upper A comma 2nd Row 1st Column Blank 2nd Column equals one eighth period left parenthesis StartRoot 5 EndRoot minus 1 right parenthesis left parenthesis 3 minus StartRoot 5 EndRoot right parenthesis b c period sine upper A comma 3rd Row 1st Column Blank 2nd Column equals one fourth period left parenthesis 4 StartRoot 5 EndRoot minus 8 right parenthesis period upper M equals left parenthesis StartRoot 5 EndRoot minus 2 right parenthesis period upper M period EndLayouthttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/481.svgupper C upper A prime upper B primehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/482.svgequals 3 period left parenthesis StartRoot 5 EndRoot minus 2 right parenthesis period upper Mhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/483.svgupper A prime upper B prime upper C Superscript prime Baseline equals left parenthesis 7 minus 3 StartRoot 5 EndRoot right parenthesis period upper Mhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/484.svgleft parenthesis a squared plus b squared right parenthesis period left parenthesis c squared plus d squared right parenthesis equals a squared c squared plus b squared d squared plus a squared d squared plus b squared c squared periodhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/485.svgStartLayout 1st Row 1st Column left parenthesis a squared plus b squared right parenthesis period left parenthesis c squared plus d squared right parenthesis 2nd Column equals a squared c squared plus b squared d squared plus a squared d squared plus b squared c squared semicolon 2nd Row 1st Column StartLayout 1st Row or else EndLayout 2nd Column StartLayout 1st Row equals a squared c squared plus b squared d squared plus 2 a c b d plus a squared d squared plus b squared c squared minus 2 a d b c comma 2nd Row equals a squared c squared plus b squared d squared minus 2 a c b d plus a squared d squared plus b squared c squared plus 2 a d b c semicolon EndLayout right brace 3rd Row 1st Column StartLayout 1st Row i period e period 2nd Row or else EndLayout 2nd Column StartLayout 1st Row equals left parenthesis a c plus b d right parenthesis squared plus left parenthesis a d minus b c right parenthesis squared comma 2nd Row equals left parenthesis a c minus b d right parenthesis squared plus left parenthesis a d plus b c right parenthesis squared period EndLayout right brace EndLayouthttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/486.svgleft parenthesis a c plus b d right parenthesishttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/487.svgleft parenthesis a d plus b c right parenthesishttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/488.svgleft parenthesis a c minus b d right parenthesishttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/489.svga left parenthesis c minus d right parenthesis minus b left parenthesis c minus d right parenthesishttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/490.svgleft parenthesis a minus b right parenthesis period left parenthesis c minus d right parenthesishttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/i_p052.webpLarge triangle with vertices A (top), B (bottom left), C (bottom right). Midpoints B' (upper right) and C' (upper left) with points D, E on BC. Interior points G, K, L, H, F, R mark cevian intersections, with solid and dashed segments forming a dense network of crossing lines and a central quadrilateral region.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/491.svgupper B prime upper Dhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/492.svgupper C prime upper Ehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/493.svg2 upper B prime upper C primehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/494.svgupper B prime upper D equals upper C prime upper Bhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/495.svgupper C prime upper E equals upper B prime upper Chttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/496.svgtherefore upper B prime upper C plus upper C prime upper B equals 2 upper B prime upper C Superscript prime Baseline periodhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/497.svgupper B prime upper Lhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/498.svgupper B prime upper Chttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/499.svgupper C prime upper L equals half upper C prime upper B periodhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/500.svgupper B upper C primehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/501.svgupper B upper Ghttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/502.svgupper C upper B primehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/503.svgupper H upper Khttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/504.svgparallel to upper B upper Chttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/505.svgupper H upper Chttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/506.svgupper C upper Khttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/507.svgupper C prime upper B Superscript prime Baseline parallel to upper B upper Chttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/508.svgbecause upper F upper G equals half upper F upper B semicolonhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/509.svgupper C prime upper L equals half upper C prime upper Bhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/510.svgupper B prime upper L equals half upper B prime upper Chttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/511.svgtherefore upper C prime upper B Superscript prime Baseline equals half sum of upper C prime upper B comma upper B prime upper Chttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/512.svgupper C prime upper B plus upper B prime upper C equals 2 upper B prime upper C primehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/513.svgupper C prime upper B equals upper B prime upper D comma and upper B prime upper C equals upper C prime upper Ehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/514.svgtherefore upper B prime upper D plus upper C prime upper E equals 2 upper B prime upper C primehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/515.svgStartFraction 11 Over 24 times 12 EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/516.svgStartFraction 11 Over 288 EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/517.svg7 and one halfhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/518.svg29 and StartFraction 277 Over 288 EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/519.svgn period left parenthesis n plus 4 right parenthesishttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/520.svgStartLayout 1st Row 1st Column Blank 2nd Column therefore the left parenthesis n plus 1 right parenthesis th term is left parenthesis n plus 1 right parenthesis period left parenthesis n plus 5 right parenthesis equals left parenthesis n plus 1 right parenthesis period left brace left parenthesis n plus 2 right parenthesis plus 3 right brace comma 2nd Row 1st Column Blank 2nd Column equals left parenthesis n plus 1 right parenthesis period left parenthesis n plus 2 right parenthesis plus 3 left parenthesis n plus 1 right parenthesis semicolon 3rd Row 1st Column Blank 2nd Column therefore upper S Subscript n Baseline equals StartFraction n period left parenthesis n plus 1 right parenthesis period left parenthesis n plus 2 right parenthesis Over 3 EndFraction plus 3 dot StartFraction n period left parenthesis n plus 1 right parenthesis Over 2 EndFraction plus upper C semicolon and upper C equals 0 semicolon 4th Row 1st Column Blank 2nd Column therefore upper S Subscript n Baseline equals n period left parenthesis n plus 1 right parenthesis period left parenthesis StartFraction n plus 2 Over 3 EndFraction plus three halves right parenthesis equals StartFraction n period left parenthesis n plus 1 right parenthesis period left parenthesis 2 n plus 13 right parenthesis Over 6 EndFraction period EndLayouthttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/521.svgupper S 100 equals StartFraction 100.101 .213 Over 6 EndFraction equals StartFraction 100.101 .71 Over 2 EndFraction equals StartFraction 100.7171 Over 2 EndFraction equals StartFraction 717100 Over 2 EndFraction equals 358550https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/i_p054.webpA circle centered at origin O with horizontal X-axis and vertical Y-axis. Points B (upper left), C (upper right), D (lower left), and E (lower right) lie on the circle, forming an inscribed trapezoid with BC parallel to DE, symmetrically placed about the Y-axis.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/522.svgupper D upper E equals xhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/523.svgtherefore upper B upper C equals 2 xhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/524.svgequals 3 x period left parenthesis StartRoot r squared minus x squared EndRoot plus StartRoot r squared minus 4 x squared EndRoot right parenthesis equals maxhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/525.svgv equals x period left parenthesis StartRoot r squared minus x squared EndRoot plus StartRoot r squared minus 4 x squared EndRoot right parenthesis equals maxhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/526.svgStartLayout 1st Row therefore StartFraction d v Over d x EndFraction equals StartRoot r squared minus x squared EndRoot plus StartRoot r squared minus 4 x squared EndRoot minus x squared period left parenthesis StartFraction 1 Over StartRoot r squared minus x squared EndRoot EndFraction plus StartFraction 4 Over StartRoot r squared minus 4 x squared EndRoot EndFraction right parenthesis equals 0 semicolon 2nd Row therefore left parenthesis r squared minus x squared right parenthesis period StartRoot r squared minus 4 x squared EndRoot plus left parenthesis r squared minus 4 x squared right parenthesis period StartRoot r squared minus x squared EndRoot equals x squared period left parenthesis 4 StartRoot r squared minus x squared EndRoot plus StartRoot r squared minus 4 x squared EndRoot right parenthesis semicolon 3rd Row therefore left parenthesis r squared minus 2 x squared right parenthesis period StartRoot r squared minus 4 x squared EndRoot equals minus left parenthesis r squared minus 8 x squared right parenthesis period StartRoot r squared minus x squared EndRoot semicolon 4th Row therefore r Superscript 4 Baseline minus 4 left parenthesis r squared x squared plus 4 x Superscript 4 Baseline right parenthesis period left parenthesis r squared minus 4 x squared right parenthesis equals left parenthesis r Superscript 4 Baseline minus 16 r squared x squared plus 64 x Superscript 4 Baseline right parenthesis period left parenthesis r squared minus x squared right parenthesis semicolon 5th Row therefore r Superscript 6 Baseline minus 8 r Superscript 4 Baseline x squared plus 20 r squared x Superscript 4 Baseline minus 16 x Superscript 6 Baseline equals r Superscript 6 Baseline minus 17 r Superscript 4 Baseline x squared plus 80 r squared x Superscript 4 Baseline minus 64 x Superscript 6 Baseline semicolon EndLayouthttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/527.svgr Superscript 6https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/528.svgx squaredhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/529.svgStartLayout 1st Row 1st Column 48 x Superscript 4 minus 60 r squared x squared plus 9 r Superscript 4 2nd Column equals 0 semicolon 2nd Row 1st Column i period e period 16 x Superscript 4 Baseline minus 20 r squared x squared plus 3 r Superscript 4 Baseline 2nd Column equals 0 semicolon EndLayouthttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/530.svgtherefore StartFraction x squared Over r squared EndFraction equals StartFraction 20 plus or minus StartRoot 208 EndRoot Over 32 EndFraction equals StartFraction 5 minus StartRoot 13 EndRoot Over 8 EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/i_p055a.webpA circle with external point A to the left. Two secants are drawn from A: one passing through chord points B and E (lower), and another through B and D (upper), with C marked on the lower secant inside the circle.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/531.svgangle upper D upper B upper E equals angle upper Ahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/i_p055b.webpA circle with external point A to the left. A secant from A passes through chord points B and E (horizontal diameter line), with C marked at center. A second line from A meets the circle at D (top).https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/532.svgangle upper D upper B upper Ehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/533.svgangle upper Ahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/i_p056.webpA regular pentagon with vertices A (top), B (left), C (right), E (upper left), L (upper right) inscribed in a circle. All diagonals drawn, intersecting at center O and interior points F, G, H, A', B', C', M, D, K, forming a pentagram with a central inner pentagon and dense crossing segments.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/534.svgk colon 1https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/535.svgl colon 1https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/536.svgm colon 1https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/537.svgupper B upper D perpendicular upper B upper Ahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/538.svgupper B upper E perpendicular upper B upper Chttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/539.svg1 minus m colon 1 minus khttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/540.svgupper F upper G perpendicular upper B upper Ahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/541.svgupper F upper H perpendicular upper B upper Chttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/542.svgupper F upper G colon upper F upper H colon colon 1 minus m colon 1 minus khttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/543.svgupper C upper Ohttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/544.svgupper C upper Ahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/545.svg1 minus l colon 1 minus khttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/546.svgupper O upper A acutehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/547.svgupper O upper B acutehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/548.svgupper O upper C acutehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/549.svgupper O upper A acute colon upper O upper B acute colon upper O upper C acute colon colon 1 minus k colon 1 minus l colon 1 minus mhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/550.svgupper O upper K colon upper O upper A acute colon colon 1 colon 1 minus khttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/551.svgupper O upper Khttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/552.svgupper O upper B primehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/553.svgupper O upper C primehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/554.svgStartLayout 1st Row 1st Column Now 2nd Column upper O upper K colon upper O upper A Superscript prime Baseline colon colon 1 colon 1 minus k semicolon 2nd Row 1st Column Blank 2nd Column upper O upper A Superscript prime Baseline colon upper O upper B Superscript prime Baseline colon colon 1 minus k colon 1 minus l semicolon 3rd Row 1st Column therefore 2nd Column upper O upper K colon upper O upper B Superscript prime Baseline colon colon 1 colon 1 minus l semicolon EndLayouthttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/555.svgupper O upper K colon upper O upper C Superscript prime Baseline colon colon 1 colon 1 minus mhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/556.svgupper A prime upper K colon upper O upper K colon colon upper O upper K minus upper O upper A Superscript prime Baseline colon upper O upper K colon colon k colon 1https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/557.svgupper B prime upper L colon radius colon colon l colon 1https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/558.svgupper C prime upper M colon radius colon colon m colon 1https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/i_p057.webpA triangle with vertices A (top left), B (bottom left), C (bottom right). Interior point D lies centrally with cevians from each vertex. Points C' (on AB, upper left), B' (on AC, middle right), and E (on AB below C') are marked, with dashed lines from D and B extending toward C.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/559.svgupper C prime upper Dhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/560.svgupper C prime upper Bhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/561.svgupper D upper B Superscript prime Baseline equals upper B prime upper Chttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/562.svgangle upper D upper B upper C Superscript prime Baseline equals 45 degreehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/563.svgangle upper B prime upper D upper C equals angle upper B prime upper C upper D periodhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/564.svgupper C upper E perpendicular upper A upper Bhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/565.svgangle upper B prime upper D upper C equals angle upper D upper C upper Ehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/566.svgangle upper B prime upper C upper D equals angle upper D upper C upper Ehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/567.svgangle upper A upper C upper Ehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/568.svgangle upper A upper B upper D equals 45 degreehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/569.svgupper B prime upper D upper C prime perpendicular upper A upper Bhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/570.svgangle upper C prime upper D upper B equals pi minus left parenthesis angle upper D upper C prime upper B plus angle upper C prime upper B upper D right parenthesis equals 45 degree equals angle upper C prime upper B upper Dhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/571.svgtherefore upper C prime upper D equals upper C prime upper Bhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/i_p058a.webpTriangle ABC with cevians concurrent at D and harmonic points B', C', E.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/572.svgStartLayout 1st Row 1st Column Blank 2nd Column Also angle upper B prime upper D upper C equals angle upper D upper C upper E equals angle upper D upper C upper B Superscript prime Baseline semicolon 2nd Row 1st Column Blank 2nd Column therefore upper D upper B Superscript prime Baseline equals upper B prime upper C semicolon 3rd Row 1st Column Blank 2nd Column therefore upper C prime upper B Superscript prime Baseline equals sum of upper B upper C Superscript prime Baseline comma upper C upper B Superscript prime Baseline period EndLayouthttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/573.svggreater than 90 degreehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/574.svgangle upper Bhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/575.svgless than 45 degreehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/576.svgangle upper Chttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/577.svgless thanhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/578.svgless than left parenthesis 45 degree minus StartFraction upper A Over 2 EndFraction right parenthesishttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/i_p058b.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/579.svgangle upper A equals 30https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/580.svgangle upper D equals 60https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/581.svgupper D upper B equals upper D upper C right parenthesis equals 1https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/582.svgupper A upper B equals xhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/583.svgcosine upper A equals StartFraction StartRoot 3 EndRoot Over 2 EndFraction equals StartFraction 2 x squared minus 1 Over 2 x squared EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/584.svgtherefore StartFraction StartRoot 3 EndRoot Over 2 EndFraction equals 1 minus StartFraction 1 Over 2 x squared EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/585.svgtherefore StartFraction 1 Over 2 x squared EndFraction equals StartFraction 2 minus StartRoot 3 EndRoot Over 2 EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/586.svgtherefore x squared equals StartFraction 1 Over 2 minus StartRoot 3 EndRoot EndFraction equals 2 plus StartRoot 3 EndRoothttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/587.svgpi period left parenthesis 2 plus StartRoot 3 EndRoot right parenthesishttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/588.svgpihttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/589.svgpi period StartFraction 2 plus StartRoot 3 EndRoot Over 12 EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/590.svgStartFraction pi Over 6 EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/591.svgequals pi period StartFraction 4 plus StartRoot 3 EndRoot Over 12 EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/592.svgupper A upper B upper C equals one half period left parenthesis 2 plus StartRoot 3 EndRoot right parenthesis period one halfhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/593.svgequals StartFraction 2 plus StartRoot 3 EndRoot Over 4 EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/594.svgupper D upper B upper C equals StartFraction StartRoot 3 EndRoot Over 4 EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/595.svgequals StartFraction 2 plus 2 StartRoot 3 EndRoot Over 4 EndFraction equals StartFraction 1 plus StartRoot 3 EndRoot Over 2 EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/596.svgequals pi period StartFraction 4 plus StartRoot 3 EndRoot Over 12 EndFraction minus StartFraction 1 plus StartRoot 3 EndRoot Over 2 EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/597.svgequals StartFraction 4 plus StartRoot 3 EndRoot Over 12 EndFraction minus StartFraction 1 plus StartRoot 3 EndRoot Over 2 pi EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/598.svgequals StartFraction 5 dot 732 Over 12 EndFraction minus StartStartFraction 2 dot 732 OverOver left parenthesis StartFraction 44 Over 7 EndFraction right parenthesis EndEndFraction equals dot 478 minus StartFraction dot 248 Over left parenthesis four sevenths right parenthesis EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/599.svgequals dot 478 minus StartFraction 1 dot 736 Over 4 EndFraction equals dot 478 minus dot 434 equals dot 044https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/600.svg1 times four ninths equals four ninthshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/601.svg1 times one ninth equals one ninthhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/602.svgtwo thirds times 1 equals two thirdshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/603.svgtwo thirds times one ninth equals two twenty seventhshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/604.svgone third times 1 equals one thirdhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/605.svgone third times four ninths equals four twenty seventhshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/606.svgone fourth comma one sixteenth comma three eighths comma one twenty fourth comma three sixteenths comma one twelfthhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/607.svgone fourth times 1 comma one sixteenth times 1 comma three eighths times two thirds comma one twenty fourth times two thirds comma three sixteenths times one third comma one twelfth times one thirdhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/608.svgStartFraction 36 plus 9 plus 36 plus 4 plus 9 plus 4 Over 9 times 16 EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/609.svgequals StartFraction 98 Over 9 times 16 EndFraction equals StartFraction 49 Over 72 EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/610.svgleft parenthesis 2 times 10 minus ModifyingAbove x minus 1 With quotation dash right parenthesis period StartFraction x Over 2 EndFraction equals 14 plus left brace 2 times 2 plus ModifyingAbove x minus 1 With quotation dash period 2 right brace dot StartFraction x Over 2 EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/611.svgStartFraction 21 x Over 2 EndFraction minus StartFraction x squared Over 2 EndFraction equals 14 plus x plus x squaredhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/612.svgtherefore 3 x squared minus 19 x plus 28 equals 0https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/613.svgtherefore x equals StartFraction 19 plus or minus 5 Over 6 EndFraction equals 4https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/614.svgseven thirdshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/615.svgy equalshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/616.svgleft parenthesis 14 plus 6 right parenthesishttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/617.svgtherefore 19 plus y period eight twelfths equals 20 plus y period six twelfthshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/618.svgy period two thirds equals 1 plus y period one half semicolon therefore y equals 6https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/i_p061.webpA triangle with vertices A (top), B (bottom left), C (bottom right). Vertical altitude AD drops from A to base point D. Points F (on AB) and E (on AC) connect down to H and G on BC respectively, forming two smaller symmetric triangles BFH and EGC flanking the central altitude, with H and G marked on the base.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/619.svgupper F upper B upper Dhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/620.svgupper E upper D upper Chttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/621.svgtherefore upper F upper H colon upper A upper D colon colon upper B upper D colon upper B upper C commahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/622.svgand upper E upper G colon upper A upper D colon colon upper D upper C colon upper B upper C semicolonhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/623.svgtherefore left parenthesis upper F upper H plus upper E upper G right parenthesis colon upper A upper D colon colon upper B upper C colon upper B upper C semicolonhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/624.svgtherefore upper F upper H plus upper E upper G equals upper A upper Dhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/625.svgupper A upper E upper Dhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/626.svgupper A upper F upper Dhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/627.svgupper D upper H equals upper D upper Ghttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/i_p062.webpA triangle with vertices A (top), B (bottom left), C (bottom right). Vertical altitude AD drops to base with E just right of D. Points G (on AB) and F (on AC) drop vertical altitudes to K and H on BC respectively, forming two smaller triangles BGK and FHC symmetrically flanking the central altitude, with K, D, E, H marked along the base.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/628.svgupper C upper E equals upper B upper Dhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/629.svgupper G upper Khttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/630.svgupper G upper B upper Ehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/631.svgupper F upper E upper Chttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/632.svgtherefore upper G upper K colon upper A upper D colon colon upper B upper E colon upper B upper C commahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/633.svgand upper F upper H colon upper A upper D colon colon upper E upper C colon upper B upper C semicolonhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/634.svgtherefore left parenthesis upper G upper K plus upper F upper H right parenthesis colon upper A upper D colon colon upper B upper C colon upper B upper C semicolonhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/635.svgtherefore upper G upper K plus upper F upper H equals upper A upper Dhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/636.svgAlso upper B upper K colon upper B upper E colon colon upper B upper D colon upper B upper C semicolonhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/637.svgtherefore upper B upper K colon upper D upper C colon colon upper E upper C colon upper B upper C semicolonhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/638.svgcolon colon upper H upper C colon upper D upper C semicolonhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/639.svgtherefore upper B upper K equals upper H upper Chttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/640.svgupper W upper W upper W upper Whttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/641.svgupper W upper W upper W upper Bhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/642.svgupper W upper B upper B upper B commahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/643.svgone eighthhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/644.svgthree eighthshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/645.svgone eighth dot 1https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/646.svgthree eighths dot one halfhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/647.svgthree eighths dot one sixthhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/648.svgthree sixteenthshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/649.svgone sixteenthhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/650.svgone third dot 1 plus one half dot one halfhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/651.svgseven twelfthshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/652.svgupper B upper B upper B upper Bhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/653.svgStartFraction 1 comma 4 comma 6 comma 4 comma 1 Over 16 EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/654.svgone sixteenth dot 1https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/655.svgone fourth dot one halfhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/656.svgone sixth dot three eighthshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/657.svgone fourth dot 1 plus one half dot one halfhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/658.svgupper A prime upper B prime upper C primehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/i_p063.webpA large inverted triangle with vertices C' (top left), B' (top right), and A' (bottom). Inner triangle ABC is inscribed with A (top center), B (middle left), and C (middle right).https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/659.svgangle upper C upper B upper A prime equals 90 degree minus StartFraction upper B Over 2 EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/660.svgtherefore upper A prime equals 180 degree minus left parenthesis upper C upper B upper A prime plus upper B upper C upper A prime right parenthesis equals StartFraction upper B plus upper C Over 2 EndFraction equals 90 degree minus StartFraction upper A Over 2 EndFraction semicolonhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/661.svgtherefore upper B upper A prime equals a period StartStartFraction cosine StartFraction upper C Over 2 EndFraction OverOver cosine StartFraction upper A Over 2 EndFraction EndEndFraction periodhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/662.svgupper B upper C Superscript prime Baseline equals c period StartStartFraction cosine StartFraction upper A Over 2 EndFraction OverOver cosine StartFraction upper C Over 2 EndFraction EndEndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/663.svgStartLayout 1st Row 1st Column therefore upper A prime upper C prime 2nd Column equals StartStartFraction a cosine squared StartFraction upper C Over 2 EndFraction plus c cosine squared StartFraction upper A Over 2 EndFraction OverOver cosine StartFraction upper A Over 2 EndFraction cosine StartFraction upper C Over 2 EndFraction EndEndFraction equals StartStartFraction a period StartFraction s period left parenthesis s minus c right parenthesis Over a b EndFraction plus c period StartFraction s period left parenthesis s minus a right parenthesis Over b c EndFraction OverOver StartFraction s Over b EndFraction dot StartRoot StartFraction left parenthesis s minus a right parenthesis period left parenthesis s minus c right parenthesis Over a c EndFraction EndRoot EndEndFraction comma 2nd Row 1st Column Blank 2nd Column equals StartStartFraction s minus c plus s minus a OverOver sine StartFraction upper B Over 2 EndFraction EndEndFraction equals StartStartFraction b OverOver sine StartFraction upper B Over 2 EndFraction EndEndFraction period EndLayouthttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/i_p064.webpInverted triangle A'B'C' with inscribed inner triangle ABC and cevians from A.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/664.svgupper A prime upper B Superscript prime Baseline equals StartStartFraction c OverOver sine StartFraction upper C Over 2 EndFraction EndEndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/665.svgupper A prime upper B prime upper C Superscript prime Baseline equals StartStartFraction b c cosine StartFraction upper A Over 2 EndFraction OverOver 2 sine StartFraction upper B Over 2 EndFraction sine StartFraction upper C Over 2 EndFraction EndEndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/666.svgStartLayout 1st Row 1st Column therefore StartFraction area of upper A prime upper B prime upper C Superscript prime Baseline Over area of upper A upper B upper C EndFraction 2nd Column equals StartStartFraction b c cosine StartFraction upper A Over 2 EndFraction OverOver 2 sine StartFraction upper B Over 2 EndFraction sine StartFraction upper C Over 2 EndFraction EndEndFraction dot StartFraction 2 Over b c sine upper A EndFraction comma 2nd Row 1st Column Blank 2nd Column equals StartStartFraction cosine StartFraction upper A Over 2 EndFraction OverOver sine StartFraction upper B Over 2 EndFraction sine StartFraction upper C Over 2 EndFraction .2 sine StartFraction upper A Over 2 EndFraction cosine StartFraction upper A Over 2 EndFraction EndEndFraction comma 3rd Row 1st Column Blank 2nd Column equals StartStartFraction 1 OverOver 2 sine StartFraction upper A Over 2 EndFraction sine StartFraction upper B Over 2 EndFraction sine StartFraction upper C Over 2 EndFraction EndEndFraction comma 4th Row 1st Column Blank 2nd Column equals StartFraction a b c Over 2 left parenthesis s minus a right parenthesis period left parenthesis s minus b right parenthesis period left parenthesis s minus c right parenthesis EndFraction period EndLayouthttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/i_p065.webpA triangle with vertices A (top), B (bottom left), C (bottom right). Cevian BD runs from B up to point D on AC, and cevian CE runs from C up to point E on AB.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/667.svgupper B upper F upper Dhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/668.svgupper C upper F upper Ehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/669.svgupper F upper B equals upper F upper Chttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/670.svgupper A upper E upper F upper Dhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/671.svgupper F upper B upper Chttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/672.svgupper F upper B upper C equalshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/673.svgStartLayout 1st Row 1st Column therefore Triangle upper D upper B upper C 2nd Column equals Triangle upper A upper E upper C comma 2nd Row 1st Column Blank 2nd Column equals Triangle upper A upper B upper C minus Triangle upper E upper B upper C semicolon EndLayouthttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/674.svgtherefore Triangles upper D upper B upper C comma upper E upper B upper C comma together equals Triangle upper A upper B upper C semicolonhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/675.svgtherefore one half dot StartFraction a squared Over cotangent theta plus cotangent upper C EndFraction plus one half dot StartFraction a squared Over cotangent theta plus cotangent upper B EndFraction equals one half dot StartFraction a squared Over cotangent upper B plus cotangent upper C EndFraction semicolonhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/676.svgtherefore StartFraction 1 Over cotangent theta plus cotangent upper C EndFraction plus StartFraction 1 Over cotangent theta plus cotangent upper B EndFraction equals StartFraction 1 Over cotangent upper B plus cotangent upper C EndFraction semicolonhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/677.svgtherefore StartFraction 2 cotangent theta plus left parenthesis cotangent upper B plus cotangent upper C right parenthesis Over cotangent squared theta plus cotangent theta dot left parenthesis cotangent upper B plus cotangent upper C right parenthesis plus cotangent upper B cotangent upper C EndFraction equals do period semicolonhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/678.svgtherefore cotangent squared theta plus cotangent theta dot left parenthesis cotangent upper B plus cotangent upper C right parenthesis plus cotangent upper B cotangent upper C equals 2 cotangent theta dot left parenthesis cotangent upper B plus cotangent upper C right parenthesis plus left parenthesis cotangent upper B plus cotangent upper C right parenthesis squared semicolonhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/679.svgtherefore cotangent squared theta minus cotangent theta period left parenthesis cotangent upper B plus cotangent upper C right parenthesis minus left parenthesis cotangent squared upper B plus cotangent upper B cotangent upper C plus cotangent squared upper C right parenthesis equals 0 semicolonhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/680.svgtherefore cotangent theta equals one half period left brace cotangent upper B plus cotangent upper C plus or minus square root left parenthesis 5 cotangent squared upper B plus 6 cotangent upper B cotangent upper C plus 5 cotangent squared upper C right parenthesis right bracehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/681.svgStartFraction 1 Over k EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/682.svgleft parenthesis 10 Superscript n Baseline minus 1 right parenthesishttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/683.svgequals StartFraction 1 Over k EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/684.svg10 Superscript mhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/685.svgleft parenthesis a Superscript n Baseline minus 1 right parenthesishttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/686.svgone seventh equals dot ModifyingAbove 1 With dot 4285 ModifyingAbove 7 With dot equals StartFraction 142857 Over 10 Superscript 6 Baseline minus 1 EndFraction periodhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/687.svgn equals 6https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/688.svgone ninth equals dot ModifyingAbove 0 With dot ModifyingAbove 7 With dot equals StartFraction 7 Over 8 squared minus 1 EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/689.svgn equals 2https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/690.svgone thirteenth equals dot ModifyingAbove 0 With dot 3524563142 ModifyingAbove 1 With dot equals StartFraction 35245631421 Over 7 Superscript 12 Baseline minus 1 EndFraction periodhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/691.svgn equals 12https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/692.svgleft parenthesis n plus 1 right parenthesishttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/693.svgStartLayout 1st Row 1st Column The chance of one failure 2nd Column is StartFraction n minus 1 Over n EndFraction semicolon 2nd Row 1st Column therefore right double quotation mark right double quotation mark n failures 2nd Column is left parenthesis StartFraction n minus 1 Over n EndFraction right parenthesis Superscript n Baseline 3rd Row 1st Column Blank 2nd Column equals left parenthesis 1 minus StartFraction 1 Over n EndFraction right parenthesis Superscript n Baseline period EndLayouthttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/694.svgm equals StartFraction 1 Over n EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/695.svgn equals StartFraction 1 Over 0 EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/696.svgequals left parenthesis 1 minus m right parenthesis Superscript StartFraction 1 Over m EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/697.svgleft parenthesis 1 minus 0 right parenthesis Superscript StartFraction 1 Over 0 EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/698.svgequals 1 minus left parenthesis 1 minus 0 right parenthesis Superscript StartFraction 1 Over 0 EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/699.svgleft parenthesis 1 plus 0 right parenthesis Superscript StartFraction 1 Over 0 EndFraction Baseline equals ehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/700.svghttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/701.svge equals a plus bhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/702.svgleft parenthesis 1 minus 0 right parenthesis Superscript StartFraction 1 Over 0 EndFraction Baseline equals a minus b equals 2 a minus ehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/703.svgStartLayout 1st Row 1st Column Now a 2nd Column equals 1 plus StartFraction 1 Over vertical bar ModifyingBelow 2 With quotation dash EndFraction plus StartFraction 1 Over vertical bar ModifyingBelow 4 With quotation dash EndFraction plus ampersand c period 2nd Row 1st Column 1 2nd Column equals 1 3rd Row 1st Column StartFraction 1 Over vertical bar ModifyingBelow 2 With quotation dash EndFraction 2nd Column equals dot 5 4th Row 1st Column StartFraction 1 Over vertical bar ModifyingBelow 4 With quotation dash EndFraction 2nd Column equals dot 04166666 ampersand c period 5th Row 1st Column StartFraction 1 Over vertical bar ModifyingBelow 6 With quotation dash EndFraction 2nd Column equals dot 00138888 ampersand c period 6th Row 1st Column StartFraction 1 Over vertical bar ModifyingBelow 8 With quotation dash EndFraction 2nd Column equals dot 00002480 ampersand c period 7th Row 1st Column StartFraction 1 Over vertical bar ModifyingBelow 10 With quotation dash EndFraction 2nd Column equals dot 00000027 8th Row 1st Column Blank 2nd Column c period 9th Row 1st Column Blank 2nd Column em dash em dash em dash em dash em dash em dash em dash em dash em dash em dash 10th Row 1st Column therefore a 2nd Column equals 1 dot 5430806 ampersand c period 11th Row 1st Column therefore 2 a 2nd Column equals 3 dot 0861612 ampersand c period 12th Row 1st Column e 2nd Column equals 2 dot 7182818 ampersand c period 13th Row 1st Column Blank 2nd Column em dash em dash em dash em dash em dash em dash em dash em dash em dash em dash 14th Row 1st Column therefore left parenthesis 1 minus 0 right parenthesis Superscript StartFraction 1 Over 0 EndFraction 2nd Column equals dot 3678793 ampersand c period 15th Row 1st Column therefore Ans period 2nd Column equals 1 minus left parenthesis 1 minus 0 right parenthesis Superscript StartFraction 1 Over 0 EndFraction Baseline equals dot 6321207 ampersand c period EndLayouthttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/i_p068.webpLeft: triangle ABC with interior points F, E, D marking cevian intersections. Right: larger triangle A'B'C' with three circles centered at F', E', D', each passing through two vertices, overlapping at interior point and illustrating the corresponding circle construction for the cevian configuration.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/704.svgupper D prime upper E prime upper F primehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/705.svgupper D primehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/706.svgupper E prime upper F primehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/707.svgupper F prime upper D primehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/708.svgupper D prime upper E primehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/709.svgupper B prime upper D prime upper C primehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/710.svgupper B upper D upper Chttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/i_p069.webpTwo circles of equal size intersecting at two points, with the intersection region overlapping centrally. A horizontal baseline runs through B' (far left) to C' (far right). Points L and M lie on the baseline, with vertical segments LG and MH and horizontal connector GKH above, all meeting near central intersection point D'.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/711.svgupper K upper D primehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/712.svgupper D primehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/713.svgupper B prime upper D prime upper C prime perpendicular upper K upper D primehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/714.svgupper G upper Lhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/715.svgupper H upper Mhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/716.svgperpendicular upper B prime upper C primehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/717.svgupper L upper D Superscript prime Baseline colon upper D prime upper M colon colon upper G upper K colon upper K upper H colon colon upper B upper D colon upper D upper C periodhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/718.svgupper B prime upper D primehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/719.svgupper D prime upper C primehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/720.svgupper L upper D primehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/721.svgupper D prime upper Mhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/722.svgtherefore upper B prime upper D prime colon upper D prime upper C prime colon colon upper B upper D colon upper D upper C periodhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/723.svgupper B prime upper F primehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/724.svgupper C prime upper E primehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/725.svgupper A primehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/726.svgupper A prime upper F prime upper B primehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/727.svgupper A prime upper E prime upper C primehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/728.svg0 comma 0 comma 0https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/729.svgx period left parenthesis StartFraction 1 Over y EndFraction minus StartFraction 1 Over z EndFraction right parenthesis equals y minus zhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/730.svgtherefore x equals y z period StartFraction y minus z Over z minus y EndFraction equals minus y zhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/731.svgy equals zhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/732.svgx equals StartFraction 0 Over 0 EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/733.svgx equals x y minus y zhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/734.svgy not equals zhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/735.svgx equals x y plus xhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/736.svgtherefore x y equals 0https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/737.svgx z equals 0https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/738.svgy not equals zhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/739.svgy equals 0https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/740.svgz equals 0https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/741.svgx equals 0https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/742.svgy equals z equals 0https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/743.svgy z equals 0https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/744.svgStartLayout 1st Row 1st Column x 2nd Column equals y equals 0 semicolon z has any value semicolon 2nd Row 1st Column x 2nd Column equals z equals 0 semicolon y has any value period EndLayouthttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/745.svgy equals zhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/746.svgStartFraction x Over y EndFraction equals x minus yhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/747.svgtherefore y squared equals x period left parenthesis y minus 1 right parenthesis semicolon i period e period x equals StartFraction y squared Over y minus 1 EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/748.svgx equals StartFraction z squared Over z minus 1 EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/749.svgx equals StartFraction k squared Over k minus 1 EndFraction comma y equals z equals khttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/750.svgy squared minus x y plus x equals 0 commahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/751.svgleft parenthesis x squared minus 4 x right parenthesis greater than 0https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/752.svgupper C primehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/753.svgupper H upper Jhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/754.svgupper D upper E equals alphahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/755.svgupper F upper G equals betahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/756.svgupper H upper J equals gammahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/i_p071.webpThree large circles mutually intersecting, forming a curved triangular outer boundary with points F, G (left), H, J (right), and D, E (top). Inner triangle B'C'A' is inscribed with numerous cevians and chords connecting A, B, C, D, E, K, creating a dense triangulated network at the center.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/757.svgupper B prime upper Dhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/758.svgupper C prime upper Ehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/759.svgupper C prime upper K perpendicular upper B prime upper Dhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/760.svgupper C upper K equals alphahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/761.svgupper B prime upper C prime equals ahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/762.svgupper B prime upper K equals b minus chttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/763.svgtherefore upper C prime upper K equals square root left brace a squared minus left parenthesis b minus c right parenthesis squared right brace semicolonhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/764.svgi period e period alpha equals square root left brace left parenthesis a minus b plus c right parenthesis period left parenthesis a plus b minus c right parenthesis right brace semicolonhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/765.svgsimilarly comma beta equals square root left brace left parenthesis a plus b minus c right parenthesis period left parenthesis negative a plus b plus c right parenthesis right brace commahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/766.svgand gamma equals square root left brace left parenthesis negative a plus b plus c right parenthesis period left parenthesis a minus b plus c right parenthesis right brace semicolonhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/767.svgtherefore StartFraction beta gamma Over alpha EndFraction equals negative a plus b plus c semicolonhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/768.svgsimilarly comma StartFraction gamma alpha Over beta EndFraction equals a minus b plus c commahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/769.svgand StartFraction alpha beta Over gamma EndFraction equals a plus b minus c semicolonhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/770.svgtherefore their sum equals a plus b plus c commahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/771.svgequals semi hyphen perimeter of upper A upper B upper C periodhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/772.svgStartFraction StartRoot 3 EndRoot Over 2 EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/773.svgStartFraction StartRoot 3 EndRoot Over 2 EndFraction comma 1https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/774.svgequals left parenthesis three fourths plus 1 minus three fourths right parenthesis dot StartFraction 1 Over StartRoot 3 EndRoot EndFraction equals StartFraction 1 Over StartRoot 3 EndRoot EndFraction semicolonhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/775.svgequals StartFraction StartRoot 2 EndRoot Over StartRoot 3 EndRoot EndFraction equalshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/776.svgequals one third dot StartFraction StartRoot 2 EndRoot Over StartRoot 3 EndRoot EndFraction dot StartFraction StartRoot 3 EndRoot Over 4 EndFraction equals StartFraction StartRoot 2 EndRoot Over 12 EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/777.svgStartRoot 2 EndRoothttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/778.svgStartFraction StartRoot 2 EndRoot Over 2 EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/779.svgone third dot StartFraction StartRoot 2 EndRoot Over 2 EndFraction equals StartFraction StartRoot 2 EndRoot Over 6 EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/780.svgStartFraction StartRoot 2 EndRoot Over 6 EndFraction dot StartFraction 12 Over StartRoot 2 EndRoot EndFraction equals 2https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/781.svgStartLayout 1st Row 1st Column 2 upper W counters comma 2nd Column is one fourth period 2nd Row 1st Column 1 upper W and 1 upper B comma 2nd Column is one half period 3rd Row 1st Column 2 upper B comma 2nd Column is one fourth period EndLayouthttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/782.svgStartLayout 1st Row 1st Column Blank 2nd Column 3 upper W comma 3rd Column is one fourth period 2nd Row 1st Column Blank 2nd Column 2 upper W comma 1 upper B comma 3rd Column is one half period 3rd Row 1st Column Blank 2nd Column 1 upper W comma 2 upper B comma 3rd Column is one fourth period EndLayouthttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/783.svgone fourth times 1 plus one half times two thirds plus one fourth times one third colon i period e period two thirds periodhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/784.svgStartLayout 1st Row 1st Column 3 upper W comma 2nd Column Blank 3rd Column is two thirds times one fourth semicolon 4th Column i period e period one sixth period 2nd Row 1st Column 2 upper W comma and 2nd Column 1 upper B comma 3rd Column is two thirds times one half plus one third times one fourth semicolon 4th Column i period e period five twelfths period 3rd Row 1st Column 1 upper W comma 2nd Column 2 upper B comma 3rd Column is two thirds times one fourth plus one third times one half semicolon 4th Column i period e period one third period 4th Row 1st Column 3 upper B comma 2nd Column Blank 3rd Column is one third times one fourth semicolon 4th Column i period e period one twelfth semicolon EndLayouthttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/785.svgone sixth times 1 plus five twelfths times two thirds plus one third times one third semicolon i period e period five ninths periodhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/786.svgfour ninthshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/787.svgStartLayout 1st Row 1st Column 2 upper W comma 2nd Column is 3rd Column one fourth times 1 plus one half times one third semicolon 4th Column i period e period five twelfths period 2nd Row 1st Column 1 upper W comma 1 upper B comma 2nd Column Blank 3rd Column one half times two thirds plus one fourth times two thirds semicolon 4th Column i period e period one half period 3rd Row 1st Column 2 upper B comma 2nd Column Blank 3rd Column one fourth times one third semicolon 4th Column i period e period one twelfth period EndLayouthttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/788.svgStartLayout 1st Row 1st Column 3 upper W comma 2nd Column is 3rd Column five twelfths times five ninths semicolon 4th Column i period e period StartFraction 25 Over 108 EndFraction period 2nd Row 1st Column 2 upper W comma 1 upper B comma 2nd Column Blank 3rd Column five twelfths times four ninths plus one half times five ninths semicolon 4th Column i period e period StartFraction 50 Over 108 EndFraction period 3rd Row 1st Column 1 upper W comma 2 upper B comma 2nd Column Blank 3rd Column one half times four ninths plus one twelfth times five ninths semicolon 4th Column i period e period StartFraction 29 Over 108 EndFraction period 4th Row 1st Column 3 upper B comma 2nd Column Blank 3rd Column one twelfth times four ninths semicolon 4th Column i period e period StartFraction 4 Over 108 EndFraction period EndLayouthttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/789.svgStartFraction 1 Over 108 EndFraction times left brace 25 times 1 plus 50 times two thirds plus 29 times one third right brace semicolon i period e period StartFraction 17 Over 27 EndFraction periodhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/i_p074.webpLarge triangle with vertices A (top), B (lower left), C (lower right). Multiple cevians and horizontal transversals create interior intersection points D, L, N, R, H, E. Base points S, B, F, K, M, G lie along BC, with vertical segments from D and E to the base, forming a dense grid of crossing lines and quadrilateral regions inside.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/790.svgupper A period upper M periodhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/791.svgupper H upper Dhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/792.svgupper L upper H upper Mhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/793.svgupper L upper Mhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/794.svgupper D upper Nhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/795.svgupper Rhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/796.svgupper N upper Dhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/797.svgupper S upper D upper Nhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/798.svgupper S upper Khttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/799.svgupper S upper Dhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/800.svgupper S upper Nhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/801.svgupper D upper N perpendicular upper A upper Chttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/802.svgupper D upper Hhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/803.svgupper D upper L equals upper L upper Ahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/804.svgtherefore upper D upper H equals upper H upper E equals upper H upper K semicolon therefore upper D upper E equals 2 upper H upper Khttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/805.svgupper D upper F plus upper E upper G equals 2 upper H upper K semicolon therefore upper D upper F plus upper E upper G equals upper D upper Ehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/806.svgupper D upper H equals upper H upper Khttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/807.svgtherefore upper D upper Nhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/808.svgtherefore upper L upper Mhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/809.svgtherefore upper Hhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/810.svgtherefore upper H upper D equals upper H upper Khttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/811.svgStartFraction x Over 2 EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/812.svgleft parenthesis x period three halves minus 6 right parenthesishttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/813.svgthree halveshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/814.svgleft parenthesis x a minus 6 right parenthesishttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/815.svgleft parenthesis x a squared minus 6 a minus 5 right parenthesishttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/816.svgleft parenthesis x a cubed minus 6 a squared minus 5 a minus 4 right parenthesishttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/817.svgleft parenthesis x a Superscript 4 Baseline minus 6 a cubed minus 5 a squared minus 4 a minus 8 right parenthesis periodhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/818.svg5 xhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/819.svgx a Superscript 4 Baseline minus 6 a cubed minus 5 a squared minus 4 a minus 6 equals 5 xhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/820.svgtherefore x equals StartFraction 6 a cubed plus 5 a squared plus 4 a plus 6 Over a Superscript 4 Baseline minus 5 EndFraction semicolonhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/821.svgequals StartFraction left parenthesis 6.3 cubed plus 5.3 squared .2 plus 4.3 .2 squared plus 6.2 cubed right parenthesis .2 Over 3 Superscript 4 Baseline minus 5.2 Superscript 4 Baseline EndFraction semicolonhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/822.svgequals StartFraction left parenthesis 162 plus 90 plus 48 plus 48 right parenthesis .2 Over 81 minus 80 EndFraction equals 696 equals 2 l period 18 s period 0 d periodhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/i_p076.webpThree overlapping triangles sharing a central region, with outer vertices A (top), B (bottom left), C (bottom right), E (far upper right), C'' (far left), A'' (bottom center). Interior points D, U, V, Q, W, R, P, S, F, C', B', A' mark cevian and transversal intersections, forming a dense star-like projective configuration.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/823.svgupper P upper A primehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/824.svgupper P upper B primehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/825.svgupper P upper C primehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/826.svgupper A double primehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/827.svgupper C double primehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/828.svgupper A prime upper A double prime equals upper P upper A primehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/829.svgupper C prime upper C double prime equals upper P upper C primehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/830.svgupper C double primehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/831.svgupper C double prime upper D perpendicular upper A upper Chttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/832.svgupper D upper E equals upper C double prime upper Dhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/833.svgupper E upper A double primehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/834.svgupper C double prime upper Rhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/835.svgupper Qhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/836.svgupper P upper Qhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/837.svgupper P upper Shttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/838.svgupper P upper Q upper R upper S upper Phttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/839.svgupper A upper Rhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/840.svgupper A upper R equals upper D upper R plus upper A upper D equals upper D upper R plus upper A upper B prime minus upper D upper B primehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/841.svgupper D upper Rhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/842.svgupper P upper Uhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/843.svgupper P upper Vhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/844.svgupper C prime upper W perpendicular upper P upper Vhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/845.svgupper A double prime upper F perpendicular upper A upper Chttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/846.svgupper D upper R colon upper R upper F colon colon upper D upper E colon upper A double prime upper F colon colon upper C double prime upper D colon upper A double prime upper Fhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/847.svgtherefore upper D upper R colon upper D upper F colon colon upper C double prime upper D colon left parenthesis upper C double prime upper D plus upper A double prime upper F right parenthesishttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/848.svgtherefore upper D upper R equals StartFraction upper D upper F dot upper C double prime upper D Over upper C double prime upper D plus upper A upper F EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/849.svgangle upper C prime upper V upper P equals upper A semicolon therefore angle upper C prime upper P upper V equals 90 degree negative upper Ahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/850.svgtherefore upper W upper P equals gamma sine upper Ahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/851.svgtherefore upper D upper B Superscript prime Baseline comma which equals 2 upper W upper P comma equals 2 gamma sine upper Ahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/852.svgupper B prime upper F equals 2 alpha sine upper Chttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/853.svgtherefore upper D upper F equals 2 left parenthesis alpha sine upper C plus gamma sine upper A right parenthesishttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/854.svgupper C prime upper W equals gamma cosine upper Ahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/855.svgtherefore upper C double prime upper D comma which equals 2 upper C prime upper W plus upper P upper B Superscript prime Baseline comma equals 2 gamma cosine upper A plus betahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/856.svgupper A double prime upper F equals 2 alpha cosine upper C plus betahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/857.svgtherefore upper C double prime upper D plus upper A double prime upper F equals 2 left parenthesis alpha cosine upper C plus gamma cosine upper A plus beta right parenthesishttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/858.svgtherefore upper D upper R equals StartFraction left parenthesis alpha sine upper C plus gamma sine upper A right parenthesis dot left parenthesis 2 gamma cosine upper A plus beta right parenthesis Over alpha cosine upper C plus gamma cosine upper A plus beta EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/859.svgupper A upper B Superscript prime Baseline equals upper B prime upper U plus upper U upper A equals upper B prime upper U plus upper P upper Vhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/860.svgequals beta cotangent upper A plus gamma c o s e c upper A equals StartFraction beta cosine upper A plus gamma Over sine upper A EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/861.svgtherefore upper A upper B Superscript prime Baseline minus upper D upper B Superscript prime Baseline equals StartFraction beta cosine upper A plus gamma Over sine upper A EndFraction minus 2 gamma sine upper Ahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/862.svgequals StartFraction beta cosine upper A plus gamma left parenthesis 1 minus 2 sine squared upper A right parenthesis Over sine upper A EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/863.svgequals StartFraction beta cosine upper A plus gamma cosine 2 upper A Over sine upper A EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/864.svgupper A upper R equals upper D upper R plus upper A upper B Superscript prime Baseline minus upper D upper B primehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/865.svgtherefore upper A upper R equals StartFraction left parenthesis alpha sine upper C plus gamma sine upper A right parenthesis dot left parenthesis 2 gamma cosine upper A plus beta right parenthesis Over alpha cosine upper C plus gamma cosine upper A plus beta EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/866.svgplus StartFraction beta cosine upper A plus gamma cosine 2 upper A Over sine upper A EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/867.svgupper A upper D upper Ehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/i_p078.webpA triangle with vertices A (top right), B (bottom left), C (bottom right). A horizontal transversal cuts across the interior with points D (on AB) and E (on AC), and intermediate points G and H. Points F and J lie on base BC between B and C, with segments connecting G to F and H to J, forming a trapezoid with inner subdivisions.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/868.svgleft single quotation mark k right single quotation mark equals ratio StartFraction upper D upper E Over a EndFraction equals StartFraction upper A upper E Over b EndFraction equals StartFraction upper A upper D Over c EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/869.svgupper D upper G equals upper D upper Ehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/870.svgtherefore upper D upper G equals k ahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/871.svgtherefore upper G upper B equals c minus k a minus k chttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/872.svgtherefore StartFraction upper G upper B Over c EndFraction equals 1 minus k minus k period StartFraction a Over c EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/873.svgtherefore upper G upper F left parenthesis which equals upper G upper B period StartFraction b Over c EndFraction right parenthesis equals b minus k b minus k period StartFraction a b Over c EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/874.svgupper G upper F equals upper D upper E equals k ahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/875.svgtherefore b minus k b minus k period StartFraction a b Over c EndFraction equals k ahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/876.svgtherefore b c equals k period left parenthesis b c plus c a plus a b right parenthesishttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/877.svgtherefore k equals StartFraction b c Over b c plus c a plus a b EndFraction equals StartStartFraction StartFraction 1 Over a EndFraction OverOver StartFraction 1 Over a EndFraction plus StartFraction 1 Over b EndFraction plus StartFraction 1 Over c EndFraction EndEndFraction equals StartStartFraction StartFraction 1 Over a EndFraction OverOver m EndEndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/878.svgupper A upper D equals StartStartFraction c period StartFraction 1 Over a EndFraction OverOver m EndEndFraction semicolon upper D upper G equals StartFraction 1 Over m EndFraction equals StartStartFraction c period StartFraction 1 Over c EndFraction OverOver m EndEndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/879.svgtherefore upper G upper B left parenthesis which equals c minus upper A upper D minus upper D upper G right parenthesis equals StartStartFraction c period left parenthesis m minus StartFraction 1 Over a EndFraction minus StartFraction 1 Over c EndFraction right parenthesis OverOver m EndEndFraction equals StartStartFraction c period StartFraction 1 Over b EndFraction OverOver m EndEndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/880.svgtherefore upper A upper D colon upper D upper G colon upper G upper B colon colon StartFraction 1 Over a EndFraction colon StartFraction 1 Over c EndFraction colon StartFraction 1 Over b EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/881.svgupper D upper E equals k a equals StartFraction 1 Over m EndFraction equals StartStartFraction 1 OverOver StartFraction 1 Over a EndFraction plus StartFraction 1 Over b EndFraction plus StartFraction 1 Over c EndFraction EndEndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/i_p079.webpThree circles of varying sizes meeting at common point P: a large circle (left) with diameter through A and D, a small circle (top) with point C and F, and a medium circle (right, partially dashed) extending to H. Points G and B lie on the horizontal baseline, with multiple chords and radii radiating from P.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/882.svgupper A upper P upper Dhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/883.svgupper B upper P upper Ehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/884.svgupper C upper P upper Fhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/885.svgtherefore sine upper A upper P upper D equals sine upper B upper P upper E equals sine upper C upper P upper Fhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/886.svgStartFraction a Over upper A upper P EndFraction equals StartFraction b Over upper B upper P EndFraction equals StartFraction c Over upper C upper P EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/887.svgtherefore upper A upper P colon upper B upper P colon upper C upper P colon colon a colon b colon chttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/888.svgupper A upper G colon upper G upper B colon colon upper A upper H colon upper H upper B colon colon a colon bhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/889.svgupper C upper F perpendicularhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/890.svgupper B upper G perpendicularhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/891.svgalpha period upper B upper C equals beta period upper C upper A equals gamma period upper A upper Bhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/892.svgupper B upper C equals StartFraction 1 Over upper B upper C EndFraction comma upper C upper A equals upper C upper G equals StartFraction 1 Over upper C upper E EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/893.svgupper A upper B equals upper B upper F equals StartFraction 1 Over upper B upper D EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/894.svgtherefore StartFraction alpha Over upper B upper C EndFraction equals StartFraction beta Over upper C upper E EndFraction equals StartFraction gamma Over upper B upper D EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/895.svgupper A upper A primehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/896.svgupper B prime upper Fhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/897.svgupper C prime upper A primehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/i_p081.webpA triangle with vertices A (top), B (bottom left), C (bottom right). Medial triangle A'B'C' is inscribed with center point O inside. Points F (on AB), G (on AC), D and E (on BC) mark cevian feet. Multiple segments from vertices and medial points cross through O, forming a dense inner network of triangles and quadrilaterals.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/898.svgupper A double prime upper B double prime upper C double primehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/899.svgupper B upper D upper B prime upper Fhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/900.svgangle upper B prime upper B upper D equals angle upper B prime upper F upper Dhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/901.svgupper B prime upper F upper Dhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/902.svgupper B prime upper D sine upper D equals upper B prime upper F sine upper F semicolonhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/903.svgx sine left parenthesis upper B prime plus upper F right parenthesis equals z sine upper Fhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/904.svgtherefore x sine upper B Superscript prime Baseline cosine upper F plus x cosine upper B Superscript prime Baseline sine upper F equals z sine upper Fhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/905.svgangle upper B primehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/906.svgtherefore x sine upper B cosine upper F equals left parenthesis z plus x cosine upper B right parenthesis sine upper Fhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/907.svgtherefore cotangent upper F equals StartFraction z plus x cosine upper B Over x sine upper B EndFraction equals cotangent upper B prime upper B upper Dhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/i_p082.webpA triangle with vertices A (top), B (bottom left), C (bottom right). Medial triangle A'B'C' is inscribed with center point O inside. Points F (on AB), G (on AC), D and E (on BC) mark cevian feet. Multiple segments from vertices and medial points cross through O, forming a dense inner network of triangles and quadrilaterals.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/908.svgupper B upper D equals x cotangent upper B prime upper B upper Dhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/909.svgtherefore upper B upper D equals StartFraction z plus x cosine upper B Over sine upper B EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/910.svgupper E upper C equals StartFraction y plus x cosine upper C Over sine upper C EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/911.svgupper B upper D plus upper E upper C equals a minus xhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/912.svgtherefore StartFraction z plus x cosine upper B Over sine upper B EndFraction plus StartFraction y plus x cosine upper C Over sine upper C EndFraction equals a minus xhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/913.svgtherefore StartFraction x sine left parenthesis upper B plus upper C right parenthesis plus y sine upper B plus z sine upper C Over sine upper B sine upper C EndFraction equals a minus xhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/914.svgStartFraction x sine upper A plus y sine upper B plus z sine upper C Over sine upper B sine upper C EndFraction equals a minus xhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/915.svgStartFraction a Over x EndFraction equals StartFraction b Over y EndFraction equals StartFraction c Over z EndFraction periodhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/916.svgStartLayout 1st Row 1st Column Blank 2nd Column StartFraction a sine upper A plus b sine upper B plus c sine upper C Over sine upper B sine upper C EndFraction equals StartFraction a squared Over x EndFraction minus a semicolon 2nd Row 1st Column therefore 2nd Column StartFraction a sine upper A plus b sine upper B plus c sine upper C Over a sine upper B sine upper C EndFraction equals StartFraction a Over x EndFraction minus 1 semicolon 3rd Row 1st Column therefore 2nd Column StartFraction a Over x EndFraction equals StartFraction a sine upper A plus b sine upper B plus c sine upper C Over a sine upper B sine upper C EndFraction plus 1 period EndLayouthttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/917.svgStartFraction a Over sine upper A EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/918.svgStartFraction b Over sine upper B EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/919.svgStartFraction c Over sine upper C EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/920.svgStartLayout 1st Row 1st Column StartFraction a Over x EndFraction 2nd Column equals StartFraction a squared plus b squared plus c squared Over a b sine upper C EndFraction plus 1 semicolon 2nd Row 1st Column Blank 2nd Column equals StartFraction a squared plus b squared plus c squared Over 2 m EndFraction plus 1 equals StartFraction b Over y EndFraction equals StartFraction c Over z EndFraction period EndLayouthttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/i_p083.webpA triangle with vertices A (bottom left), B (bottom right), and C (top). Three circular arcs connect the vertices: arc from A to B (bottom, concave up), arc from A to C (left, concave right), and arc from B to C (right, concave left), all meeting at C with tick marks. Points E (left) and D (right) lie on the side arcs, with dashed lines through interior point F.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/921.svgupper A upper F upper Bhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/922.svgupper A upper E upper Chttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/923.svgupper A upper B upper D upper C upper Ehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/924.svgequals StartFraction area of semicircle Over area of fig period upper A upper B upper D upper C upper E EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/i_p084.webpA geometric figure with points A, B (base), C (apex), E, D, and F.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/925.svgupper A upper B equals 2 ahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/926.svgequals StartFraction pi a squared Over 2 EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/927.svgupper A upper B upper D upper C upper E equals 2 times sector upper A upper B upper D upper C minus Triangle upper A upper B upper Chttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/928.svgequals 2 period StartFraction 4 pi a squared Over 6 EndFraction minus StartRoot 3 EndRoot period a squared equals a squared period left parenthesis StartFraction 4 pi Over 3 EndFraction minus StartRoot 3 EndRoot right parenthesis semicolonhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/929.svgtherefore chance equals StartStartFraction StartFraction pi Over 2 EndFraction OverOver StartFraction 4 pi Over 3 EndFraction minus StartRoot 3 EndRoot EndEndFraction equals StartStartFraction 3 OverOver 8 minus StartFraction 6 StartRoot 3 EndRoot Over pi EndFraction EndEndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/930.svgLet upper K upper L equals upper M upper N equals a commahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/931.svgupper K upper N equals upper L upper M equals b commahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/932.svgupper K upper M equals upper L upper N equals c semicolonhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/933.svgupper L upper M upper Khttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/934.svgupper M upper K upper Lhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/935.svgupper K upper L upper Mhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/936.svgupper K upper Thttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/937.svgupper L upper M upper Nhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/938.svgupper K upper Rhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/939.svgupper K upper Shttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/940.svgupper M upper Nhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/941.svgupper T upper Rhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/942.svgupper T upper Mhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/943.svgupper T upper Shttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/944.svgupper T upper R upper Mhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/945.svgupper T upper S upper Mhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/946.svgone third period upper K upper T period upper L upper M upper Nhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/947.svgupper K upper T squared equals upper K upper S squared minus upper T upper S squaredhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/948.svgequals c period sine upper Bhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/i_p085a.webpA diamond-shaped polyhedron with outer vertices K (top), L (left), M (bottom), N (right). Interior points R, S, T form an inner triangle. Edges are labeled a, b, c indicating equal lengths, with multiple triangulating diagonals connecting all vertices, creating a fully triangulated faceted solid.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/949.svgupper R upper M upper S upper Thttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/950.svgupper R upper Mhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/951.svgupper M upper Shttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/952.svgangle upper R upper M upper Shttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/i_p085b.webpA small quadrilateral with vertices T (top center), R (left), S (right), and M (bottom center). Diagonal RS connects the two side vertices horizontally, with segments from R and S meeting at both T above and M below, forming two triangles sharing the diagonal RS.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/953.svgStartFraction upper T upper S Over sine upper T upper R upper S EndFraction equals StartFraction upper T upper R Over sine upper T upper S upper R EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/954.svgupper T upper S cosine upper T upper S upper R plus upper T upper R cosine upper T upper R upper S equals upper R upper Shttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/955.svgStartLayout 1st Row 1st Column therefore StartFraction upper T upper S Over sine upper T upper R upper S EndFraction 2nd Column equals StartFraction upper T upper R Over sine upper T upper S upper R EndFraction comma 2nd Row 1st Column Blank 2nd Column equals StartFraction upper T upper S cosine upper T upper S upper R plus upper T upper R cosine upper T upper R upper S Over sine upper T upper R upper S cosine upper T upper S upper R plus sine upper T upper S upper R cosine upper T upper R upper S EndFraction comma 3rd Row 1st Column Blank 2nd Column equals StartFraction upper R upper S Over sine upper R upper M upper S EndFraction equals StartFraction upper M upper S Over sine upper M upper R upper S EndFraction semicolon 4th Row 1st Column therefore StartFraction upper T upper S Over cosine upper M upper R upper S EndFraction 2nd Column equals StartFraction upper M upper S Over sine upper M upper R upper S EndFraction semicolon i period e period upper T upper S equals upper M upper S cotangent upper M upper R upper S period EndLayouthttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/956.svgcotangent upper M upper R upper Shttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/957.svgtangent upper M upper R upper Shttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/i_p086.webpA plain triangle with vertex R at the upper left, S at the upper right, and M at the bottom center. The triangle is scalene and undecorated, with bold labeled vertices and no interior markings.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/958.svgupper R upper M upper Shttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/959.svgStartLayout 1st Row 1st Column tangent upper M upper R upper S 2nd Column equals StartFraction sine upper M upper R upper S Over cosine upper M upper R upper S EndFraction equals StartFraction upper R upper S sine upper M upper R upper S Over upper R upper S cosine upper M upper R upper S EndFraction comma 2nd Row 1st Column Blank 2nd Column equals StartFraction upper M upper S sine upper R upper M upper S Over upper R upper M minus upper M upper S cosine upper R upper M upper S EndFraction period EndLayouthttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/960.svgupper T upper S equals upper M upper S cotangent upper M upper R upper S semicolonhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/961.svgcotangent upper M upper R upper S equals StartFraction upper R upper M minus upper M upper S cosine upper R upper M upper S Over upper M upper S sine upper R upper M upper S EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/962.svgequals StartFraction c cosine upper A minus c cosine upper B cosine upper C Over c cosine upper B sine upper C EndFraction equals StartFraction cosine upper A minus cosine upper B cosine upper C Over cosine upper B sine upper C EndFraction semicolonhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/963.svgtherefore upper T upper S equals StartFraction c Over sine upper C EndFraction dot left parenthesis cosine upper A minus cosine upper B cosine upper C right parenthesishttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/964.svgupper K upper T squared equals upper K upper S squared minus upper T upper S squaredhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/965.svgtherefore it equals left parenthesis c sine upper B right parenthesis squared minus StartFraction c squared Over sine squared upper C EndFraction dot left parenthesis cosine upper A minus cosine upper B cosine upper C right parenthesis squaredhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/966.svgequals StartFraction c squared Over sine squared upper C EndFraction dot left brace left parenthesis sine upper B sine upper C right parenthesis squared minus left parenthesis cosine upper A minus cosine upper B cosine upper C right parenthesis squared right bracehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/967.svgupper K upper T equals StartFraction c Over sine upper C EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/968.svgStartRoot sine squared upper B sine squared upper C minus cosine squared upper B cosine squared upper C minus cosine squared upper A plus 2 cosine upper A cosine upper B cosine upper C EndRoothttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/969.svgequals StartFraction c Over sine upper C EndFraction multiplied byhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/970.svgStartRoot left parenthesis 1 minus cosine squared upper B right parenthesis dot left parenthesis 1 minus cosine squared upper C right parenthesis minus cosine squared upper B cosine squared upper C minus cosine squared upper A plus 2 cosine upper A cosine upper B cosine upper C EndRoothttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/971.svgStartFraction c Over sine upper C EndFraction dot StartRoot 1 minus left parenthesis cosine squared upper A plus cosine squared upper B plus cosine squared upper C right parenthesis plus 2 cosine upper A cosine upper B cosine upper C EndRoothttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/i_p087a.webpA diamond-shaped polyhedron with outer vertices K (top), L (left), M (bottom), N (right) and interior triangle R, S, T. All vertices are connected by triangulating segments radiating from apex K down through R, T, S to M. Edges labeled a, b, c indicate equal lengths on corresponding sides.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/972.svgupper L upper M upper N equals StartFraction a b sine upper C Over 2 EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/973.svgequals StartFraction a b c Over 6 EndFraction period StartRoot 1 minus left parenthesis cosine squared upper A plus cosine squared upper B plus cosine squared upper C right parenthesis plus 2 cosine upper A cosine upper B cosine upper C EndRoot periodhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/974.svgangle upper B upper A upper D equals thetahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/975.svgangle upper C upper A upper D equals phihttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/i_p087b.webpA bold triangle with vertices A (top right), B (bottom left), C (bottom right). Cevian AD drops from A to point D on base BC. Interior point B' lies on AB and D' lies near the center, connected by a dashed line from B' to D'.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/976.svgStartFraction sine left parenthesis upper B plus theta right parenthesis Over sine theta EndFraction equals StartStartFraction c OverOver left parenthesis StartFraction m a Over m plus n EndFraction right parenthesis EndEndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/977.svgequals StartFraction c period left parenthesis m plus n right parenthesis Over m a EndFraction semicolonhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/978.svgtherefore sine upper B cotangent theta plus cosine upper B equals StartFraction c period left parenthesis m plus n right parenthesis Over m a EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/979.svgtherefore cotangent theta equals StartFraction c period left parenthesis m plus n right parenthesis Over m a period sine upper B EndFraction minus cotangent upper B commahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/980.svgequals StartFraction left parenthesis m plus n right parenthesis period left parenthesis a cosine upper B plus b cosine upper A right parenthesis minus m a cosine upper B Over m a sine upper B EndFraction commahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/981.svgequals StartFraction left parenthesis m plus n right parenthesis b cosine upper A plus n a cosine upper B Over m a sine upper B EndFraction semicolonhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/i_p088.webpA geometric diagram of triangle ABC with interior points B', D, D' and dashed lines.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/982.svgi period e period cotangent theta equals StartStartFraction left parenthesis m plus n right parenthesis dot StartFraction b Over sine upper B EndFraction dot cosine upper A plus n a cotangent upper B OverOver m a EndEndFraction commahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/983.svgequals StartFraction left parenthesis m plus n right parenthesis a cotangent upper A plus n a cotangent upper B Over m a EndFraction commahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/984.svgequals StartFraction left parenthesis m plus n right parenthesis cotangent upper A plus n cotangent upper B Over m EndFraction periodhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/985.svgcotangent phi equals StartFraction left parenthesis m plus n right parenthesis cotangent upper A plus m cotangent upper C Over n EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/986.svgm cotangent theta minus n cotangent phi equals n cotangent upper B minus m cotangent upper Chttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/987.svgStartFraction cotangent upper B plus cotangent phi Over cotangent upper C plus cotangent theta EndFraction equals StartFraction m Over n EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/988.svgcotangent theta equals StartFraction m plus 2 n Over m EndFraction period StartFraction 1 Over StartRoot 3 EndRoot EndFraction commahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/989.svgcotangent phi equals StartFraction n plus 2 m Over n EndFraction dot StartFraction 1 Over StartRoot 3 EndRoot EndFraction semicolonhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/990.svgtherefore StartFraction cotangent theta Over cotangent phi EndFraction equals StartFraction m n plus 2 n squared Over m n plus 2 m squared EndFraction semicolonhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/991.svgtherefore StartFraction tangent theta Over tangent phi EndFraction equals StartFraction m n plus 2 m squared Over m n plus 2 n squared EndFraction semicolonhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/992.svgupper C upper D prime upper B primehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/993.svgStartFraction upper B prime upper D prime Over upper D prime upper C EndFraction equals StartFraction m n plus 2 m squared Over m n plus 2 n squared EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/994.svgStartFraction m Over n EndFraction equals one halfhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/995.svgStartFraction upper B prime upper D prime Over upper D prime upper C EndFraction equals two fifthshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/996.svgtangent upper A equals 1 comma tangent upper B equals 2 comma tangent upper C equals 3https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/997.svgcotangent theta equals StartFraction m plus n plus n period one half Over m EndFraction equals StartFraction 2 m plus 3 n Over 2 m EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/998.svgcotangent phi equals StartFraction m plus n plus m period one third Over n EndFraction equals StartFraction 3 n plus 4 m Over 3 n EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/999.svgtherefore StartFraction tangent theta Over tangent phi EndFraction equals StartFraction 6 m n plus 8 m squared Over 6 m n plus 9 n squared EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1000.svgStartFraction tangent theta Over tangent phi EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1001.svgStartFraction m Over n EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1002.svg2 left parenthesis 6 m n plus 9 n squared right parenthesis minus 3 left parenthesis 6 m n plus 8 m squared right parenthesis equals 0 commahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1003.svgleft parenthesis upper B squared minus 4 upper A upper C right parenthesishttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1004.svgleft parenthesis 1 squared plus 4.4 .3 right parenthesishttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1005.svg4 m squared plus m n minus 3 n squared equals 0https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1006.svgStartFraction m Over n EndFraction equals StartFraction negative 1 plus or minus 7 Over 8 EndFraction equals three fourthshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1007.svgStartFraction upper B prime upper D prime Over upper D prime upper C EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1008.svgtwo thirdshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1009.svgStartFraction upper B upper D Over upper D upper C EndFraction equals three fourthshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1010.svgleft parenthesis a squared plus 4 b squared plus 4 c squared right parenthesis plus left parenthesis 4 a squared plus b squared plus 4 c squared right parenthesishttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1011.svgplus left parenthesis 4 a squared plus 4 b squared plus c squared right parenthesis equals 9 left parenthesis a squared plus b squared plus c squared right parenthesishttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1012.svga squared plus b squared plus c squaredhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1013.svgStartLayout 1st Row 1st Column Blank 2nd Column equals one ninth dot left brace left parenthesis a squared plus 4 b squared plus 4 c squared right parenthesis plus left parenthesis 4 a squared plus b squared plus 4 c squared right parenthesis plus left parenthesis 4 a squared plus 4 b squared plus c squared right parenthesis right brace semicolon 2nd Row 1st Column Blank 2nd Column equals one ninth dot left brace left parenthesis a squared plus 4 b squared plus 4 c squared plus 8 b c minus 4 c a minus 4 a b right parenthesis 3rd Row 1st Column Blank 2nd Column plus left parenthesis 4 a squared plus b squared plus 4 c squared minus 4 b c plus 8 c a minus 4 a b right parenthesis 4th Row 1st Column Blank 2nd Column plus left parenthesis 4 a squared plus 4 b squared plus c squared minus 4 b c minus 4 c a plus 8 a b right parenthesis right brace semicolon 5th Row 1st Column Blank 2nd Column equals one ninth dot left brace left parenthesis negative a plus 2 b plus 2 c right parenthesis squared plus left parenthesis 2 a minus b plus 2 c right parenthesis squared plus left parenthesis 2 a plus 2 b minus c right parenthesis squared right brace semicolon 6th Row 1st Column Blank 2nd Column equals left parenthesis StartFraction negative a plus 2 b plus 2 c Over 3 EndFraction right parenthesis squared plus left parenthesis StartFraction 2 a minus b plus 2 c Over 3 EndFraction right parenthesis squared plus left parenthesis StartFraction 2 a plus 2 b minus c Over 3 EndFraction right parenthesis squared period EndLayouthttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1014.svgNow left parenthesis negative a plus 2 b plus 2 c right parenthesis equals 3 left parenthesis b plus c right parenthesis minus left parenthesis a plus b plus c right parenthesishttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1015.svga plus b plus chttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1016.svgleft parenthesis negative a plus 2 b plus 2 c right parenthesishttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1017.svgtherefore StartFraction negative a plus 2 b plus 2 c Over 3 EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1018.svgStartFraction negative a plus 2 b plus 2 c Over 3 EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1019.svgStartFraction negative a plus 2 b plus 2 c Over 3 EndFraction equals ahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1020.svgnegative a plus 2 b plus 2 c equals 3 ahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1021.svgb plus c equals 2 ahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1022.svgStartFraction negative a plus 2 b plus 2 c Over 3 EndFraction equals bhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1023.svgnegative a plus 2 b plus 2 c equals 3 bhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1024.svg2 c equals a plus bhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1025.svgStartFraction negative a plus 2 b plus 2 c Over 3 EndFraction equals chttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1026.svgnegative a plus 2 b plus 2 c equals 3 chttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1027.svg2 b equals c plus ahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1028.svga squaredhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1029.svgb squaredhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1030.svgc squaredhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1031.svgleft parenthesis StartFraction negative a plus 2 b plus 2 c Over 3 EndFraction right parenthesis squaredhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1032.svgleft parenthesis StartFraction 2 a minus b plus 2 c Over 3 EndFraction right parenthesis squaredhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1033.svgleft parenthesis StartFraction 2 a plus 2 b minus c Over 3 EndFraction right parenthesis squaredhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1034.svg1 squaredhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1035.svg4 squaredhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1036.svg5 squaredhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1037.svg2 squaredhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1038.svg3 squaredhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1039.svg8 squaredhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1040.svg7 squaredhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1041.svg6 squaredhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1042.svg9 squaredhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/i_p091.webpA triangle with vertices A (bottom left), B (bottom right), and an implied apex, with line EC crossing diagonally from upper right down through interior point P. Points D (on AP), G and E (above P), F and H (on base AB) mark intersections, with dashed lines from P to H.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1043.svgupper P upper Dhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1044.svgupper E upper Phttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1045.svgupper A upper D equals upper D upper Ehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1046.svgupper D upper Phttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1047.svgtherefore upper F upper P equals upper P upper Ehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1048.svgupper G upper P upper Hhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1049.svgangle upper P upper F upper H greater than angle upper P upper E upper Ghttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1050.svgupper P upper F upper Hhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1051.svgupper P upper E upper Ghttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1052.svgupper P upper F equals upper P upper Ehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1053.svgangle upper F upper P upper H equals angle upper G upper P upper E comma and angle upper P upper F upper H greater than angle upper P upper E upper G commahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1054.svgtherefore upper P upper H greater than upper P upper Ghttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1055.svgTriangle upper P upper F upper H greater than Triangle upper P upper G upper Ehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1056.svgupper A upper F upper P upper Ghttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1057.svgtherefore Triangle upper A upper G upper H greater than Triangle upper A upper E upper Fhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1058.svgupper A upper E upper Fhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/i_p092.webpA three-dimensional parallelepiped with outer vertices A, B, D (top face), E, F, G (bottom face). An inner rectangular box is inscribed with vertices C, J, L (upper) and O, H, K, M (lower). Multiple diagonal segments connect outer and inner vertices.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1059.svgupper L upper G equals StartRoot 3 EndRoothttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1060.svgupper M upper G equals left parenthesis StartRoot 2 EndRoot minus 1 right parenthesishttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1061.svgtherefore upper L upper M left parenthesis equals upper J upper K right parenthesis equals NestedStartRoot 3 minus left parenthesis 2 plus 1 minus 2 StartRoot 2 EndRoot right parenthesis NestedEndRoothttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1062.svgequals 2 Superscript three fourthshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1063.svgtherefore upper O upper J equals upper O upper K equals StartFraction 1 Over 2 Superscript one fourth Baseline EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1064.svgupper J upper Khttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1065.svgupper C upper D upper Ghttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1066.svgx cosine alpha plus y cosine beta plus z cosine gamma minus p equals 0 commahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1067.svghttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1068.svgupper L upper Ghttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1069.svgupper X upper Zhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1070.svgx cosine alpha plus z cosine gamma minus p equals 0 semicolonhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1071.svgleft parenthesis 1 comma StartFraction 1 Over 2 Superscript one fourth Baseline EndFraction right parenthesishttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1072.svgleft parenthesis StartRoot 2 EndRoot comma minus StartFraction 1 Over 2 Superscript one fourth Baseline EndFraction right parenthesishttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1073.svgtherefore cosine alpha plus StartFraction 1 Over 2 Superscript one fourth Baseline EndFraction dot cosine gamma minus p equals 0https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1074.svgStartRoot 2 EndRoot dot cosine alpha minus StartFraction 1 Over 2 Superscript one fourth Baseline EndFraction dot cosine gamma minus p equals 0https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1075.svgtherefore left parenthesis StartRoot 2 EndRoot minus 1 right parenthesis dot cosine alpha equals StartFraction 2 Over 2 Superscript one fourth Baseline EndFraction dot cosine gamma equals 2 Superscript three fourths Baseline dot cosine gammahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1076.svgtherefore StartFraction cosine alpha Over 2 Superscript three fourths Baseline EndFraction equals StartFraction cosine gamma Over StartRoot 2 EndRoot minus 1 EndFraction equals StartFraction 1 Over StartRoot 2 Superscript three halves Baseline plus 3 minus 2 Superscript three halves Baseline EndRoot EndFraction equals StartFraction 1 Over StartRoot 3 EndRoot EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1077.svgtherefore cosine alpha equals StartFraction 2 Superscript three fourths Baseline Over StartRoot 3 EndRoot EndFraction comma cosine gamma equals StartFraction StartRoot 2 EndRoot minus 1 Over StartRoot 3 EndRoot EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1078.svgtherefore p equals StartFraction 2 Superscript three fourths Baseline Over StartRoot 3 EndRoot EndFraction plus StartFraction StartRoot 2 EndRoot minus 1 Over 2 Superscript one fourth Baseline dot StartRoot 3 EndRoot EndFraction equals StartFraction StartRoot 2 EndRoot plus 1 Over 2 Superscript one fourth Baseline dot StartRoot 3 EndRoot EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1079.svgupper C upper D upper G equals StartRoot 3 EndRoothttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1080.svgupper O comma equals StartFraction StartRoot 2 EndRoot plus 1 Over 3 dot 2 Superscript one fourth Baseline EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1081.svgStartFraction 8 left parenthesis StartRoot 2 EndRoot plus 1 right parenthesis Over 3 dot 2 Superscript one fourth Baseline EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1082.svgStartFraction 4 Over 3 dot 2 Superscript one fourth Baseline EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1083.svgStartFraction 8 Over 3 dot 2 Superscript one fourth Baseline EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1084.svgStartFraction 8 left parenthesis 2 plus StartRoot 2 EndRoot right parenthesis Over 3 dot 2 Superscript one fourth Baseline EndFraction equals StartFraction 8 dot 2 Superscript one fourth Baseline dot left parenthesis StartRoot 2 EndRoot plus 1 right parenthesis Over 3 EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/i_p094.webpLeft: triangle ABC circumscribes a circle centered at O, with contact points D, E, F and additional labeled points R, Q, S, P, M, N on sides and circle. Right: a separate circle contains inscribed quadrilateral GHLK with diagonals drawn, illustrating related circle-polygon theorems.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1085.svgupper O upper Dhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1086.svgupper O upper Ehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1087.svgupper O upper Fhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1088.svgupper G upper K perpendicularhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1089.svgupper G upper H upper Khttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1090.svgupper K upper Lhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1091.svgupper L upper Hhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1092.svgtherefore upper L upper Hhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1093.svgThen sqs of upper M upper D comma upper D upper O equals sqs of upper P upper E comma upper E upper O semicolonhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1094.svgalso sq period of upper L upper H equals sqs of upper R upper F comma upper F upper O semicolonhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1095.svgtherefore sqs of upper M upper D comma upper D upper O comma upper L upper H equals sqs of upper P upper E comma upper R upper F comma upper E upper O comma upper F upper O semicolonhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1096.svgbut sqs of upper D upper O comma upper L upper H equals sqs of upper K upper L comma upper L upper H commahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1097.svgequals sqs of upper G upper H comma upper G upper K equals sqs of upper E upper O comma upper F upper O semicolonhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1098.svgtherefore sq period of upper M upper D equals sqs of upper P upper E comma upper R upper F semicolonhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1099.svgtherefore 4 times sq period of upper M upper D equals 4 times sqs of upper P upper E comma upper R upper F semicolonhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1100.svgi period e period sq period of upper M upper N equals sqs of upper P upper Q comma upper R upper S periodhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1101.svgupper R upper Shttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1102.svgStartFraction 1 Over x EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1103.svgStartFraction 1 Over y EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1104.svgStartFraction 1 Over z EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1105.svgStartFraction 1 Over x EndFraction plus StartFraction 1 Over y EndFraction plus StartFraction 1 Over z EndFraction equals one half semicolonhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1106.svgx equals 3https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1107.svgStartFraction 1 Over y EndFraction plus StartFraction 1 Over z EndFraction equals one sixthhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1108.svgStartFraction 1 Over y EndFraction equals StartFraction k Over k plus l EndFraction times one sixthhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1109.svgStartFraction l Over k plus l EndFraction times one sixthhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1110.svgStartFraction k Over k plus l EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1111.svgStartFraction l Over k plus l EndFraction commahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1112.svgStartFraction 1 Over y EndFraction be not less than StartFraction 1 Over z EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1113.svgStartFraction k Over k plus l EndFraction not less than one halfhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1114.svgone half comma so that StartFraction l Over k plus l EndFraction equals one halfhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1115.svgStartFraction 1 Over x EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1116.svgStartFraction 1 Over y EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1117.svgStartFraction 1 Over z EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1118.svgone third comma one twelfth comma one twelfth semicolon one third comma one ninth comma one eighteenth semicolon one third comma one eighth comma one twenty fourth semicolon one third comma one tenth comma one fifteenth semicolon one third comma one seventh comma one forty second periodhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1119.svgx equals 4https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1120.svgStartFraction 1 Over y EndFraction plus StartFraction 1 Over z EndFraction equals one fourthhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1121.svgStartFraction l Over k plus l EndFraction equals one halfhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1122.svgfour fifthshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1123.svgone fifthhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1124.svgStartFraction 1 Over z EndFraction commahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1125.svgone fourth comma one eighth comma one eighth semicolon one fourth comma one sixth comma one twelfth semicolon one half comma one fifth comma one twentieth periodhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1126.svgx equals 5https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1127.svgStartFraction 1 Over y EndFraction plus StartFraction 1 Over z EndFraction equals three tenthshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1128.svgone fifth comma one fifth comma one tenth semicolon one fifth comma one fourth comma one twentieth semicolonhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1129.svgx equals 6https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1130.svgStartFraction 1 Over y EndFraction plus StartFraction 1 Over z EndFraction equals one thirdhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1131.svgthree fourths comma one fourth periodhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1132.svgone sixth comma one sixth comma one sixth semicolon one sixth comma one fourth comma one twelfth semicolonhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1133.svgStartFraction 1 Over y EndFraction plus StartFraction 1 Over z EndFraction greater than one thirdhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1134.svggreater than one sixthhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1135.svgless than 6https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1136.svg51 and three seventhshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1137.svg8 and four seventhshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1138.svgleft parenthesis 1 minus x right parenthesishttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1139.svgx times 1 plus left parenthesis 1 minus x right parenthesis times one halfhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1140.svgStartLayout 1st Row 1st Column therefore x plus StartFraction 1 minus x Over 2 EndFraction 2nd Column equals k semicolon therefore x equals 2 k minus 1 semicolon 2nd Row 1st Column Blank 2nd Column therefore left parenthesis 1 minus x right parenthesis equals 2 minus 2 k period EndLayouthttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1141.svgleft parenthesis 2 k minus 1 right parenthesis times 1https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1142.svgleft parenthesis 2 minus 2 k right parenthesis times one halfhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1143.svg2 k minus 1https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1144.svg1 minus khttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1145.svgStartFraction 2 k minus 1 Over k EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1146.svgStartFraction 1 minus k Over k EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1147.svgStartLayout 1st Row 1st Column is 2nd Column StartFraction 2 k minus 1 Over k EndFraction times 1 plus StartFraction 1 minus k Over k EndFraction times one half semicolon 2nd Row 1st Column i period e period 2nd Column StartFraction 3 k minus 1 Over 2 k EndFraction period EndLayouthttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1148.svgStartFraction 3 k minus 1 Over 2 k EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1149.svgStartFraction 3 k minus 1 Over 2 k EndFraction into StartStartFraction 3 times StartFraction 3 k minus 1 Over 2 k EndFraction minus 1 OverOver 2 times StartFraction 3 k minus 1 Over 2 k EndFraction EndEndFraction semicolon i period e period into StartFraction 7 k minus 3 Over 6 k minus 2 EndFraction periodhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1150.svgk comma StartFraction 3 k minus 1 Over 2 k EndFraction comma StartFraction 7 k minus 3 Over 6 k minus 2 EndFraction commahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1151.svgStartFraction k minus 0 Over 0 times k minus left parenthesis negative 1 right parenthesis EndFraction comma StartFraction 3 k minus 1 Over 2 k minus 0 EndFraction comma StartFraction 7 k minus 3 Over 6 k minus 2 EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1152.svgStartFraction left parenthesis 2 Superscript n Baseline minus 1 right parenthesis times k minus left parenthesis 2 Superscript n minus 1 Baseline minus 1 right parenthesis Over left parenthesis 2 Superscript n Baseline minus 2 right parenthesis times k minus left parenthesis 2 Superscript n minus 1 Baseline minus 2 right parenthesis EndFraction commahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1153.svgStartFraction 3 k minus 1 Over 2 k EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1154.svgStartStartFraction 3 times StartFraction left parenthesis 2 Superscript n Baseline minus 1 right parenthesis times k minus left parenthesis 2 Superscript n minus 1 Baseline minus 1 right parenthesis Over left parenthesis 2 Superscript n Baseline minus 2 right parenthesis times k minus left parenthesis 2 Superscript n minus 1 Baseline minus 2 right parenthesis EndFraction minus 1 OverOver 2 times StartFraction left parenthesis 2 Superscript n Baseline minus 1 right parenthesis times k minus left parenthesis 2 Superscript n minus 1 Baseline minus 1 right parenthesis Over left parenthesis 2 Superscript n Baseline minus 2 right parenthesis times k minus left parenthesis 2 Superscript n minus 1 Baseline minus 2 right parenthesis EndFraction EndEndFraction semicolonhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1155.svgi period e period StartFraction k times left parenthesis 3 dot 2 Superscript n Baseline minus 3 minus 2 Superscript n Baseline plus 2 right parenthesis minus 3 dot 2 Superscript n minus 1 Baseline plus 3 plus 2 Superscript n minus 1 Baseline minus 2 Over left parenthesis 2 Superscript n plus 1 Baseline minus 2 right parenthesis times k minus left parenthesis 2 Superscript n Baseline minus 2 right parenthesis EndFraction semicolonhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1156.svgi period e period StartFraction left parenthesis 2 Superscript n plus 1 Baseline minus 1 right parenthesis times k minus left parenthesis 2 Superscript n Baseline minus 1 right parenthesis Over left parenthesis 2 Superscript n plus 1 Baseline minus 2 right parenthesis times k minus left parenthesis 2 Superscript n Baseline minus 2 right parenthesis EndFraction semicolonhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1157.svgModifyingAbove n plus 1 With quotation dash vertical bar Superscript th Baselinehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1158.svg1 Superscript sthttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1159.svg2 Superscript ndhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1160.svg3 Superscript rdhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1161.svgModifyingAbove m plus 1 With quotation dash vertical bar Superscript th Baselinehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1162.svgStartFraction left parenthesis 2 Superscript m plus 1 Baseline minus 1 right parenthesis times k minus left parenthesis 2 Superscript m Baseline minus 1 right parenthesis Over left parenthesis 2 Superscript m plus 1 Baseline minus 2 right parenthesis times k minus left parenthesis 2 Superscript m Baseline minus 2 right parenthesis EndFraction periodhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1163.svgStartLayout 1st Row 1st Column Then chance is 2nd Column StartFraction left parenthesis 2 Superscript m plus 1 Baseline minus 1 right parenthesis times alpha minus left parenthesis 2 Superscript m Baseline minus 1 right parenthesis dot left parenthesis alpha plus beta right parenthesis Over left parenthesis 2 Superscript m plus 1 Baseline minus 2 right parenthesis times alpha minus left parenthesis 2 Superscript m Baseline minus 2 right parenthesis dot left parenthesis alpha plus beta right parenthesis EndFraction semicolon 2nd Row 1st Column i period e period 2nd Column StartFraction left parenthesis 2 Superscript m plus 1 Baseline minus 2 Superscript m Baseline right parenthesis alpha minus left parenthesis 2 Superscript m Baseline minus 1 right parenthesis dot beta Over left parenthesis 2 Superscript m plus 1 Baseline minus 2 Superscript m Baseline right parenthesis alpha minus left parenthesis 2 Superscript m Baseline minus 2 right parenthesis dot beta EndFraction semicolon 3rd Row 1st Column i period e period 2nd Column StartFraction 2 Superscript m Baseline dot left parenthesis alpha minus beta right parenthesis plus beta Over 2 Superscript m Baseline dot left parenthesis alpha minus beta right parenthesis plus 2 beta EndFraction period EndLayouthttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1164.svgnine tenthshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1165.svgalpha equals 9https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1166.svgbeta equals 1https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1167.svgStartFraction 32 times 8 plus 1 Over 32 times 8 plus 2 EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1168.svgStartFraction 257 Over 258 EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/i_p100.webpA geometric diagram showing intersecting 3D wireframe shapes (diamond/pyramid forms) centered on perpendicular axes, with a bold diagonal line cutting through.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1169.svgupper D upper O upper Ahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1170.svgupper D prime upper Q upper A primehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1171.svgupper A prime upper L perpendicular upper X upper Yhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1172.svgupper O upper Rhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1173.svgupper L upper Nhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1174.svgupper N upper Lhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1175.svgupper L upper A primehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1176.svgupper O upper Mhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1177.svgupper M upper Rhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1178.svgx primehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1179.svgy primehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1180.svgupper O upper Ahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1181.svga primehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1182.svgangle upper X upper O upper Rhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1183.svgx squared plus y squared equals a squared left parenthesis 1 right parenthesishttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1184.svgangle upper X upper A upper C equals 150 degreehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1185.svgtherefore Equation to upper A upper C is y equals minus StartFraction 1 Over StartRoot 3 EndRoot EndFraction dot left parenthesis x minus a right parenthesishttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1186.svgi period e period x plus StartRoot 3 EndRoot dot y equals a left parenthesis 2 right parenthesishttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1187.svgStartFraction x Over cosine theta EndFraction equals StartFraction y Over sine theta EndFraction equals ahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1188.svgtherefore comma at upper R comma StartFraction x prime Over cosine theta EndFraction equals StartFraction y prime Over sine theta EndFraction equals a Superscript prime Baseline semicolon left parenthesis 3 right parenthesishttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1189.svgtherefore comma by left parenthesis 2 right parenthesis comma a prime dot cosine theta plus StartRoot 3 EndRoot dot a prime dot sine theta equals ahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1190.svgtherefore a prime equals StartFraction a Over cosine theta plus StartRoot 3 EndRoot dot sine theta EndFraction left parenthesis 4 right parenthesishttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1191.svgwhite up pointing trianglehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1192.svgupper D prime upper O upper Rhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1193.svgupper Q upper A Superscript prime Baseline colon upper Q upper D Superscript prime Baseline colon colon upper O upper R colon upper O upper D primehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1194.svga colon h colon colon StartFraction a Over cosine theta plus StartRoot 3 EndRoot dot sine theta EndFraction colon h minus zhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1195.svgtherefore h minus z equals StartFraction h Over cosine theta plus StartRoot 3 EndRoot dot sine theta EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1196.svgcosine theta equals StartFraction x Over a EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1197.svgsine theta equals StartFraction y Over a EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1198.svgtherefore h minus z equals StartFraction a h Over x plus StartRoot 3 EndRoot dot y EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1199.svgleft parenthesis x plus StartRoot 3 EndRoot dot y right parenthesis dot left parenthesis h minus z right parenthesis equals a h left parenthesis 5 right parenthesishttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1200.svg10 vhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1201.svg11 vhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1202.svgleft parenthesis x minus 1 right parenthesis dot 11 vhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1203.svgy dot 11 v minus vhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1204.svgleft parenthesis z minus 1 right parenthesis dot 11 v minus vhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1205.svgx v minus 11 vhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1206.svgy v minus vhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1207.svgz v minus 12 vhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1208.svgy equals x minus 10https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1209.svgz equals x plus 1https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1210.svgleft parenthesis x plus y plus z right parenthesis comma equals 3 x minus 9https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1211.svgleft parenthesis x plus y plus z right parenthesis period v minus 24 vhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1212.svgleft parenthesis 3 x minus 33 right parenthesis vhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1213.svgStartFraction left parenthesis 3 x minus 33 right parenthesis dot v Over 3 x minus 9 EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1214.svgtherefore left parenthesis x minus 11 right parenthesis period v equals left parenthesis x minus 3 right parenthesis period 6https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1215.svgz period 11 v equals 11 times 240https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1216.svgleft parenthesis x plus 1 right parenthesis period 11 v equals 11 times 240https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1217.svgtherefore StartFraction x minus 11 Over x plus 1 EndFraction equals StartFraction 6 period left parenthesis x minus 3 right parenthesis Over 240 EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1218.svgtherefore left parenthesis x plus 1 right parenthesis period left parenthesis x minus 3 right parenthesis equals 40 period left parenthesis x minus 11 right parenthesishttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1219.svgtherefore x squared minus 2 x minus 3 equals 40 x minus 440https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1220.svgtherefore x squared minus 42 x plus 437 equals 0https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1221.svg42 squared minus 4 times 437 equals 1764 minus 1748 equals 16https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1222.svgtherefore x equals StartFraction 42 plus or minus 4 Over 2 EndFraction equals 23 or 19https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1223.svgleft parenthesis x plus 1 right parenthesis period 11 v equals 11 times 240https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1224.svg24 v equals 240https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1225.svgtherefore v equals 10https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1226.svgangle upper B upper A upper D equals k period upper A comma angle upper C upper B upper E equals l period upper B comma angle upper A upper C upper F equals m period upper Chttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1227.svgangle upper A upper B upper E equals left parenthesis 1 minus l right parenthesis period upper Bhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1228.svgangle upper B upper C prime upper D equals angle upper C prime upper A upper B plus angle upper C prime upper B upper Ahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1229.svgk period upper A plus left parenthesis 1 minus l right parenthesis period upper B equals upper C period left parenthesis 1 right parenthesishttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1230.svgl period upper B plus left parenthesis 1 minus m right parenthesis period upper C equals upper A semicolon left parenthesis 2 right parenthesishttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1231.svgm period upper C plus left parenthesis 1 minus k right parenthesis period upper A equals upper B period left parenthesis 3 right parenthesishttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/i_p103.webpA triangle with vertices A (top), B (bottom left), C (bottom right). Medial triangle A'B'C' is inscribed with B' (upper center), C' (middle left), A' (lower center). Points F (on AB), D (on BC), and E (on AC) mark cevian feet, with multiple crossing segments connecting all labeled points, forming a dense inner network.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1232.svgStartLayout 1st Row 1st Column k 2nd Column equals f left parenthesis upper A comma upper B comma upper C comma theta right parenthesis comma 2nd Row 1st Column l 2nd Column equals f left parenthesis upper B comma upper C comma upper A comma theta right parenthesis comma 3rd Row 1st Column m 2nd Column equals f left parenthesis upper C comma upper A comma upper B comma theta right parenthesis period EndLayouthttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1233.svgk upper A minus l upper B equals upper C minus upper Bhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1234.svgupper A period f left parenthesis upper A comma upper B comma upper C comma theta right parenthesis minus upper B period f left parenthesis upper B comma upper C comma upper A comma theta right parenthesis equals upper C minus upper Bhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1235.svgStartLayout 1st Row 1st Column k period upper A 2nd Column equals x upper A plus y upper B plus z upper C plus theta comma 2nd Row 1st Column l period upper B 2nd Column equals x upper B plus y upper C plus z upper A plus theta semicolon EndLayouthttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1236.svgk upper A minus l upper B equals left parenthesis x minus z right parenthesis period upper A plus left parenthesis y minus x right parenthesis period upper B plus left parenthesis z minus y right parenthesis period upper Chttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1237.svgStartLayout 1st Row 1st Column therefore x minus z 2nd Column equals 0 semicolon i period e period x equals z semicolon 2nd Row 1st Column z minus y 2nd Column equals 1 semicolon i period e period z equals y plus 1 period EndLayouthttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1238.svgy equals 1https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1239.svgx equals z equals 2https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1240.svgStartLayout 1st Row 1st Column k upper A 2nd Column equals 2 upper A plus upper B plus 2 upper C plus theta comma 2nd Row 1st Column l upper B 2nd Column equals 2 upper B plus upper C plus 2 upper A plus theta semicolon EndLayouthttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1241.svgf left parenthesis upper A comma upper B comma upper C comma theta right parenthesis mean StartFraction 2 upper A plus upper B plus 2 upper C plus theta Over upper A EndFraction periodhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1242.svgleft parenthesis upper A plus upper B plus upper C right parenthesishttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1243.svgk equals StartFraction upper A plus upper C plus theta Over upper A EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1244.svg180 degreehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1245.svgk equals StartFraction theta minus upper B Over upper A EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/i_p104.webpA geometric diagram of triangle ABC with multiple interior points A', B', C', D, E, F and intersecting cevians.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1246.svgStartLayout 1st Row 1st Column Similarly l 2nd Column equals StartFraction theta minus upper C Over upper B EndFraction comma 2nd Row 1st Column m 2nd Column equals StartFraction theta minus upper A Over upper C EndFraction period EndLayouthttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1247.svgk upper A equals theta minus upper Bhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1248.svgupper A upper D upper Chttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1249.svgupper B upper E upper Ahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1250.svgupper C upper F upper Bhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1251.svgk upper A not greater than upper A semicolon therefore theta minus upper B not greater than upper Ahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1252.svgtheta not greater than upper A plus upper Bhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1253.svgtheta not greater thanhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1254.svgk upper A not less than 0https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1255.svgtheta minus upper B not less than 0https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1256.svgtheta not less than upper Bhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1257.svgtheta not less than upper Ahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1258.svgnot greater than 180 degree negative upper Ahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1259.svgupper B prime upper C primehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1260.svgupper A upper B upper C primehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1261.svgleft parenthesis theta minus upper B right parenthesishttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1262.svgleft parenthesis 180 degree negative theta minus upper A right parenthesishttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1263.svgleft parenthesis 180 degree negative upper C right parenthesishttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1264.svgStartLayout 1st Row 1st Column upper A upper C prime 2nd Column equals StartFraction upper A upper B Over sine upper A upper C prime upper B EndFraction period sine upper A upper B upper C prime equals StartFraction c Over sine upper C EndFraction period sine left parenthesis theta plus upper A right parenthesis equals StartFraction a Over sine upper A EndFraction period sine left parenthesis theta plus upper A right parenthesis semicolon 2nd Row 1st Column upper B upper C prime 2nd Column equals StartFraction upper A upper B Over sine upper A upper C prime upper B EndFraction period sine upper B upper A upper C prime equals StartFraction c Over sine upper C EndFraction period sine left parenthesis theta minus upper B right parenthesis equals StartFraction a Over sine upper A EndFraction period sine left parenthesis theta minus upper B right parenthesis EndLayouthttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1265.svgupper A upper B prime equals StartFraction a Over sine upper A EndFraction period sine left parenthesis theta minus upper A right parenthesishttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1266.svgupper B prime upper C prime equals upper A upper C prime minus upper A upper B primehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1267.svgStartLayout 1st Row 1st Column therefore it 2nd Column equals StartFraction a Over sine upper A EndFraction left brace sine left parenthesis theta plus upper A right parenthesis minus sine left parenthesis theta minus upper A right parenthesis right brace comma 2nd Row 1st Column Blank 2nd Column equals StartFraction a Over sine upper A EndFraction period 2 cosine theta sine upper A equals a Baseline 2 cosine theta period EndLayouthttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1268.svgStartFraction a prime Over a EndFraction equals StartFraction b prime Over b EndFraction equals StartFraction c prime Over c EndFraction equals 2 cosine thetahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1269.svgdeltahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1270.svgStartFraction StartRoot 3 EndRoot Over 2 EndFraction divided by x equals tangent 15 degreehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1271.svgtangent 15 degreehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1272.svgStartFraction 2 t Over left parenthesis 1 minus t squared right parenthesis EndFraction equals tangent 30 degree equals StartFraction 1 Over StartRoot 3 EndRoot EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1273.svgtherefore 1 minus t squared equals 2 StartRoot 3 EndRoot period t semicolon t squared plus 2 StartRoot 3 EndRoot period t minus 1 equals 0 semicolonhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1274.svgtherefore t equals StartFraction minus 2 StartRoot 3 EndRoot plus or minus 4 Over 2 EndFraction equals left parenthesis rejecting negative value right parenthesis 2 minus StartRoot 3 EndRoot periodhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1275.svgtherefore x equals StartFraction StartRoot 3 EndRoot Over 2 left parenthesis 2 minus StartRoot 3 EndRoot right parenthesis EndFraction equals StartFraction StartRoot 3 EndRoot Over 2 EndFraction left parenthesis 2 plus StartRoot 3 EndRoot right parenthesis equals StartRoot 3 EndRoot plus three halves periodhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1276.svgleft parenthesis StartRoot 3 EndRoot plus 1 right parenthesishttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1277.svgStartRoot 3 EndRoot equals 1 dot 7https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1278.svgtherefore distance equals 2 dot 7https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1279.svg2 and one halfhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1280.svgtangent Superscript negative 1 Baseline left parenthesis StartFraction StartRoot 3 EndRoot Over 2 EndFraction divided by five halves right parenthesis semicolon i period e period tangent Superscript negative 1 Baseline StartFraction StartRoot 3 EndRoot Over 5 EndFraction periodhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1281.svgStartFraction sine Over cosine EndFraction equals StartFraction StartRoot 3 EndRoot Over 5 EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1282.svgStartLayout 1st Row 1st Column Blank 2nd Column therefore StartFraction sine Over StartRoot 3 EndRoot EndFraction equals StartFraction cosine Over 5 EndFraction equals StartFraction 1 Over StartRoot 28 EndRoot EndFraction semicolon therefore sine equals StartRoot three twenty eighths EndRoot equals StartFraction StartRoot 84 EndRoot Over 28 EndFraction comma 2nd Row 1st Column Blank 2nd Column equals StartFraction rather over 9 Over 28 EndFraction semicolon StartStartFraction 7 vertical bar ModifyingBelow 9 dot With quotation dash OverOver StartFraction 4 vertical bar ModifyingBelow 1 dot 28 ampersand c period With quotation dash Over dot 32 ampersand c period EndFraction EndEndFraction EndLayouthttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1283.svgStartLayout 1st Row 1st Column Now left parenthesis by mem period tech period right parenthesis 2nd Column sine Superscript negative 1 Baseline dot 3 equals 17 dot 45 ampersand c period degree period 2nd Row 1st Column Blank 2nd Column sine Superscript negative 1 Baseline dot 4 equals 23 dot 57 ampersand c period degree period EndLayouthttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1284.svgone fifthhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1285.svg1 and one fifthhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1286.svg1 dot 20 degreehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1287.svg18 dot 65 degreehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1288.svg3 and one halfhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1289.svgleft parenthesis StartFraction StartRoot 3 EndRoot Over 2 EndFraction divided by seven halves right parenthesis semicolon i period e period StartFraction StartRoot 3 EndRoot Over 7 EndFraction semicolonhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1290.svgtherefore StartFraction sine Over StartRoot 3 EndRoot EndFraction equals StartFraction cosine Over 7 EndFraction equals StartFraction 1 Over StartRoot 52 EndRoot EndFraction semicolon therefore sine equals StartRoot three fifty seconds EndRoot equals nearly StartRoot one seventeenth EndRoothttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1291.svgStartFraction StartRoot 17 EndRoot Over 17 EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1292.svgStartRoot 17 EndRoot equals 4 dot 12 ampersand c period therefore sine equals dot 24 ampersand c periodhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1293.svgsine Superscript negative 1 Baseline dot 2 equals 11 dot 53https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1294.svg17 dot 45https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1295.svg14 dot 53https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/i_p108.webpLarge triangle with vertices A (top left), B (bottom left), C (bottom right). Two horizontal transversals cross the interior: upper one through H, G and lower through F, E, N. Interior point P marks central intersections, with base points K, L, D, M on BC.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1296.svgupper D upper E upper Fhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1297.svgupper H upper Ghttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1298.svgupper G upper Phttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1299.svgupper H upper Phttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1300.svgupper L upper Khttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1301.svgupper K upper Phttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1302.svgupper N colonhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1303.svgtherefore upper G upper P equals upper P upper L comma and upper H upper P equals upper P upper Mhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1304.svgbecause upper K upper L is parallel to upper G upper N comma and that upper L upper P equals upper P upper Ghttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1305.svgtherefore upper K upper P equals upper P upper N semicolon therefore upper M upper N is parallel to upper H upper Khttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1306.svgupper P upper G upper H comma upper P upper L upper Mhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1307.svgtherefore upper G upper H equals upper L upper M period Similarly upper K upper L equals upper G upper N comma and upper M upper N equals upper H upper Khttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1308.svgleft parenthesis alpha right parenthesis upper B upper Bhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1309.svgleft parenthesis beta right parenthesis upper B upper W comma left parenthesis gamma right parenthesis upper W upper W comma are respectively one fourth comma one half comma one fourthhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1310.svgleft parenthesis alpha right parenthesis upper B upper B upper B comma left parenthesis beta right parenthesis upper B upper W upper Bhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1311.svgleft parenthesis gamma right parenthesis upper W upper W upper Bhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1312.svgone fourthhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1313.svgone halfhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1314.svgequals one fourth dot 1 plus one half dot two thirds plus one fourth dot one third equals two thirds periodhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1315.svgupper B upper B upper Whttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/1316.svgupper B upper Whttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-2-pillow-problems/images/i_f004.webp3D coordinate axes X, Y, Z with projected parallelogram and oblique line. https://openoldbooks.com/books/curiosa-mathematica-part-i/read2026-11-15T15:48:14.650Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/1.svg2 Superscript nhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/2.svgpihttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/3.svgStartFraction 40 Over 3 EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/4.svgthree fourthshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/i_f021.webpA circle containing an inscribed square, divided by two perpendicular diameters into eight triangles, illustrating Dodgson's key axiom about the inscribed equilateral tetragon.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/5.svgalphahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/6.svgbetahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/7.svg2 Superscript ahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/8.svghttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/9.svgStartFraction 1 Over 2 Superscript a plus 3 Baseline EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/i_p003a.webpTwo straight lines intersecting at point E, horizontal line AB crossed by diagonal line CD, forming four angles. A classic Euclidean diagram illustrating intersecting lines and the angles they produce.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/i_p003b.webpTwo straight lines, horizontal line AB crossed by diagonal line CD, forming four angles.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/10.svgupper A upper Bhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/11.svgupper C upper Dhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/12.svgupper Ehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/13.svgupper Chttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/i_p005.webpTwo nested triangles sharing base AB — outer triangle ADB with apex D, inner triangle ACB with apex C sitting just below D. Illustrates a proposition comparing triangles with a common base but differing apex heights.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/14.svgupper A upper B upper Chttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/15.svgupper A upper B upper Dhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/16.svgupper A upper Dhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/17.svgupper D upper Bhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/18.svgupper A upper Chttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/19.svgupper C upper Bhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/20.svgupper Dhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/21.svgupper A upper C upper Bhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/22.svgthereforehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/23.svgupper A upper D upper Bhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/i_p006.webpTwo triangles sharing base AB — left shows equilateral-looking triangle ABC with apex C high above; right shows a flat, acute triangle ABC with internal point F, illustrating how apex position and angle affect triangle geometry.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/24.svgupper Ahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/25.svgupper B upper A upper Chttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/26.svgupper A upper C equals upper A upper Bhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/27.svgupper B upper Chttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/28.svgupper Bhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/29.svgupper A upper B upper Fhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/30.svgupper A upper B equals upper A upper Chttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/31.svgtherefore angle upper A upper C upper B equals angle upper A upper B upper Chttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/32.svgupper A upper F upper Bhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/33.svgtherefore angle upper A upper F upper B is greater than angle upper A upper B upper Fhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/i_p008.webpTwo overlapping triangles on baseline AD — triangle ACB with apex C, and triangle AEB with vertical height EB, their sides crossing at point F. Illustrates a proposition comparing areas or angles of intersecting triangles.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/34.svgupper A upper D upper Ehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/35.svgupper Fhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/36.svgupper A upper B upper Ehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/37.svgupper B upper Fhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/38.svgupper A upper Ehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/39.svgupper E upper Bhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/40.svgupper Rhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/41.svg2 upper Rhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/42.svg6 upper Rhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/43.svg3 upper Rhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/44.svgleft parenthesis 2 upper R plus a right parenthesishttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/45.svgleft parenthesis 2 upper R plus 2 a right parenthesishttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/i_p011.webpVertical line AD on the right, with point B far left and interior point C, forming triangles BAC and BDC. Lines radiate from B through C to AD, illustrating a proposition about angles or distances from an external point.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/46.svgupper B upper C upper Dhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/47.svgupper B upper C upper Ahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/48.svgupper C upper Ahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/49.svgupper B upper Dhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/50.svgupper A upper C upper Dhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/51.svgleft parenthesis 6 upper R plus 2 a right parenthesishttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/52.svg4 upper Rhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/i_p012a.webpVertical line AD on the right with midpoint C, and point B to the left, forming two symmetric triangles BAC and BDC sharing horizontal base BC, illustrating equal angles or distances about a midpoint.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/53.svgupper C upper D equals upper C upper Ahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/54.svgleft parenthesis 4 upper R plus 2 a right parenthesishttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/55.svgleft parenthesis 2 upper R comma equals left parenthesis 4 upper R plus 2 a right parenthesishttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/i_p012b.webpTwo overlapping triangles, ABC on the left with interior point D, and a larger triangle extending to E on the right, their sides crossing at D, illustrating a proposition about overlapping or congruent triangles.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/56.svgupper D upper E equals upper B upper Dhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/57.svgupper C upper Ehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/58.svgupper C upper D upper Ehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/59.svgupper D upper C upper Ehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/60.svgupper C upper E upper Dhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/61.svgupper B upper C upper Ehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/62.svgbecausehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/63.svgupper C upper B upper Dhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/i_p014.webpDiagram with inscribed square within a circle, divided by two perpendicular diameters into eight triangles, here appearing within the text to support a specific proposition about the inscribed tetragon.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/i_p015.webpA quarter-circle arc from K to B, with multiple lines radiating from corner A to labelled points K, J, H, G, F, E, D, C, B along the arc and sides, illustrating how angles or chord lengths vary progressively around a quadrant.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/64.svgupper B upper Khttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/65.svgupper F upper Khttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/66.svgupper D upper Fhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/67.svgupper F upper Hhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/68.svgupper H upper Khttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/69.svgupper A upper B upper Khttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/70.svgupper B upper C upper Khttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/i_p016.webpA quarter-circle arc from K to B, with multiple lines radiating from corner A to labelled points K, J, H, G, F, E, D, C, B along the arc and sides, illustrating how angles or chord lengths vary progressively around a quadrant.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/71.svgupper B upper D upper Chttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/72.svgupper A upper D upper Chttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/73.svgb e c a u s ehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/74.svgupper B upper F upper Khttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/75.svgupper A upper B upper F upper Khttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/76.svgupper B upper D upper Fhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/77.svgupper F upper H upper Khttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/78.svgupper A upper B upper D upper F upper H upper Khttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/79.svgupper D upper E upper Fhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/80.svgupper F upper G upper Hhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/81.svgupper H upper J upper Khttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/82.svgthetahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/i_p018.webpTwo nested triangles sharing base AB, outer triangle ADB with apex D, inner triangle ACB with apex C just below, with apexes D and C positioned nearer together.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/83.svgupper D upper A upper Bhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/84.svg2 thetahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/85.svgleft parenthesis 2 theta minus a right parenthesishttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/86.svgleft parenthesis 2 theta minus 2 a right parenthesishttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/87.svgStartFraction 2 theta minus a Over 3 EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/88.svgupper A prime upper B prime upper C primehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/89.svgupper B upper Ahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/90.svgupper C upper C primehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/i_p020.webpSymmetric diagram with baseline AA', apex D above, and central point B on the base. Inner points C and C' form a small diamond shape, with multiple lines radiating from D and B, illustrating a proposition about symmetric or mirror triangles.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/91.svgupper A upper A primehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/92.svgupper A upper A prime upper Dhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/93.svgupper B upper A prime upper C primehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/94.svgupper A prime upper C primehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/95.svgupper B upper A upper Dhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/96.svgupper B upper A prime upper Dhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/97.svgupper A upper A prime upper C prime upper Chttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/98.svgupper D upper Chttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/99.svgupper A prime upper B upper C primehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/100.svg2 left parenthesis 2 theta minus a right parenthesishttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/101.svg8 upper Rhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/102.svgleft parenthesis 8 upper R plus 4 theta minus 2 a right parenthesishttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/103.svgupper C primehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/104.svg10 upper Rhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/105.svgleft parenthesis 10 upper R plus 2 theta right parenthesishttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/106.svgleft parenthesis 10 upper R plus 4 theta minus 2 a right parenthesishttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/107.svg4 thetahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/108.svg8 thetahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/109.svg16 thetahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/110.svg16 theta equals 2 upper Rhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/i_p022.webpTwo parallel horizontal lines DE and AB, with vertical lines and diagonals connecting labelled points D, H, C, L, E above and A, G, K, B below, via intermediate points F and J, illustrating a proposition about parallel lines and transversals.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/111.svgupper C upper A upper Bhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/112.svgupper C upper B upper Ahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/113.svgupper F upper Ghttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/114.svgupper C upper Hhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/115.svgupper A upper Ghttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/116.svgupper F upper A upper Ghttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/117.svgupper F upper C upper Hhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/118.svgupper F upper Ahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/119.svgupper F upper Chttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/120.svgupper F upper H upper Chttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/121.svgupper A upper F upper G equals angle upper C upper F upper Hhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/122.svgupper A upper F upper Ghttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/123.svgupper A upper F upper Hhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/124.svgupper C upper F upper Hhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/125.svgupper G upper Fhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/126.svgupper G upper Hhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/127.svgupper D upper Ehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/128.svgupper Jhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/129.svgupper K upper Lhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/i_p024.webpA rectangle ABCD with two crossing diagonals inside, plus point C' above D and D' on the right side, illustrating a proposition about diagonals, rectangles, and points displaced from the corners.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/130.svgupper A upper B upper C upper Dhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/131.svgupper D prime upper C primehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/132.svgupper A upper C prime upper D primehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/133.svgupper A upper D equals upper B upper Chttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/134.svgupper A upper B equals upper D upper Chttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/135.svgupper A prime upper D primehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/i_p025.webpRectangle ABCD with interior point D' connected by lines to corners D and C above, and to point A' on the base, illustrating a proposition about an internal point and its distances to the sides or corners.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/136.svgupper D upper D primehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/137.svgupper D prime upper Chttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/138.svgupper A upper A prime upper D prime upper Dhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/139.svgupper D primehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/140.svgupper A prime upper D prime upper D equals angle upper A upper D upper D primehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/141.svgupper A prime upper D prime upper Chttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/142.svgupper D upper D prime upper Chttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/i_p026.webpRectangle with points F, C, E along the top and A, D, B along the base. Point C connects by lines to A, D, and B, forming triangles within, illustrating a proposition about a point on the top side and its distances to the base.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/143.svgupper A upper D upper C upper Fhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/144.svgupper B upper D upper C upper Ehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/145.svgupper F upper Dhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/146.svgupper C upper F upper Ahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/147.svgtherefore angle upper C upper A upper D equals angle upper A upper C upper Fhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/148.svgupper C upper B upper D equals angle upper B upper C upper Ehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/149.svgupper F upper C upper Ahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/i_p027.webpTwo parallel horizontal lines AB and CD, with a small triangle formed between them by points E, G above and F, H below, illustrating a proposition about transversals or angles between parallel lines.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/150.svgupper E upper Fhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/151.svgupper E upper Hhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/152.svgupper E upper F upper Hhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/153.svgupper E upper G upper Hhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/154.svgupper G upper E upper Fhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/155.svgupper G upper H upper Fhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/i_p028.webpA diagram showing multiple lines radiating from central point E toward labelled points Z, K, V, Y, T, S, R, N, H, M, B, D, F, L, C, G, A,a dense fan of rays and intersecting lines illustrating a proposition about angles, parallels, or convergence.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/156.svgupper B upper E upper Fhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/157.svgupper E upper F upper Dhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/158.svgupper F upper E upper Ghttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/159.svgupper G upper Ehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/160.svgupper Hhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/161.svgupper E upper Khttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/162.svgupper E upper Lhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/163.svgupper B upper E upper Hhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/164.svgupper B upper E upper Khttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/165.svghttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/166.svgupper E upper Mhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/167.svgupper Mhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/168.svgupper M upper Nhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/169.svgupper E upper N upper Mhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/170.svgupper E upper Nhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/171.svgupper E upper N upper Rhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/172.svgupper E upper Rhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/173.svgupper E upper R upper Shttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/174.svgupper E upper Y upper Zhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/175.svgupper M upper E upper Zhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/176.svgupper M upper E upper Hhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/177.svgupper M upper E upper Khttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/178.svgupper M upper R upper T upper Zhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/179.svgupper Vhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/180.svgupper M upper Vhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/181.svgupper M upper R upper T upper Vhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/i_p033.webpQuadrilateral CABD with crossing diagonals, plus two arcs between C and D and between D and B, illustrating a proposition about a quadrilateral, its diagonals, and the circular arcs connecting its vertices.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/182.svgupper D upper A upper Chttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/183.svgupper A upper B upper D upper Chttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/i_p034.webpAn elaboration of the previous diagram, adding points F on the top arc and E on the right arc, with additional crossing lines from A and C, illustrating a more complex proposition about arcs, chords, and intersecting diagonals.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/184.svgupper A upper B upper E upper Dhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/185.svgupper B upper E upper Dhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/186.svghttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/187.svgupper A upper Fhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/188.svgupper C upper Fhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/189.svg2 mhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/190.svgupper A upper E upper Dhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/191.svgupper B upper D upper Ehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/192.svgupper B upper Ehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/193.svgupper D upper F upper Chttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/i_p035.webpThe recurring core diagram — inscribed square within a circle divided by two perpendicular diameters into eight triangles, appearing again to support the book's central theorem about the inscribed equilateral tetragon.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/194.svgStartFraction 1 Over 2 Superscript a plus 3 Baseline EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/i_p036.webpA square ADBC with a quarter-circle arc from D to B, point C on the arc, and diagonal DB crossing the figure, illustrating a proposition about a square, its inscribed quarter-circle, and a point on the arc.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/195.svgphihttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/196.svg2 Superscript a plus 2https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/197.svg2 phihttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/198.svg4 phihttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/199.svg8 phihttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/200.svg2 Superscript a plus 3 Baseline phihttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/201.svg2 Superscript a plus 3 Baseline phi equals upper Rhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/202.svg2 Superscript a plus 2https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/203.svgStartFraction 1 Over 8192 EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/204.svgStartFraction 1 Over 2 Superscript a plus 3 Baseline EndFractionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/205.svg16 phihttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/206.svg2 Superscript a plus 4 Baseline phihttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/207.svg2 Superscript a plus 4 Baseline phi equals 2 upper Rhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/i_p046.webpCoordinate axes OX and OY with a descending curve from C through F and K to M, and stepped rectangular constructions at intervals A, D, G, illustrating convergence or limits as successive rectangles diminish toward the axis.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/208.svgupper O upper Xhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/209.svgupper O upper Yhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/210.svgy equals 2 Superscript negative xhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/211.svgupper O upper C equals upper O upper A equals upper A upper D equals upper D upper Ghttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/212.svgx equals 0https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/213.svgy equals 1https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/214.svgx equals 1https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/215.svgy equals one halfhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/216.svgx equals 2https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/217.svgy equals one fourthhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/218.svgx equals 3https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/219.svgy equals one eighthhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/220.svgupper L upper C upper F upper K upper M upper Nhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/221.svghttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/222.svghttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/223.svgupper C upper Ohttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/224.svgupper C upper O upper A upper Fhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/225.svgupper O upper Bhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/226.svgleft parenthesis upper O upper B plus upper A upper E plus ampersand c period for ever right parenthesishttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/227.svgleft parenthesis 1 plus one half plus one fourthhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/i_p049.webpFour axes meeting at centre V, vertical X1 Y1, horizontal CD, and diagonal rays X2, X3 upper-left and Y2, Y3 lower-right, dividing the plane into four numbered sectors, illustrating angular regions around a point.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/228.svgupper X 1 upper V upper Y 1https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/229.svgupper X 2 upper V upper Y 2https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/230.svgupper X 3 upper V upper Y 3https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/231.svgupper C upper V upper Dhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/232.svgupper C upper Vhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/233.svgupper V upper X 1https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/234.svgupper V upper X 2https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/235.svgupper V upper X 3https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/i_p050.webpNearly identical to previous figure but without the horizontal AB line intersecting at V, the same four sectors and radiating rays X2 ,X3 and Y2, Y3, showing a variant case of angular regions around centre point V.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/236.svgupper V upper Chttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/237.svgupper Y 1 upper Ahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/238.svgupper V upper Y 1https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/239.svgupper Y 1 upper Bhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/240.svgupper V upper Dhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/241.svgupper V upper Y 2https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/i_p052.webpA third variant of the four-sector diagram, rays X2, X3 and Y2, Y3 now spread slightly wider apart from centre V, with sectors 1, 2, 3, 4 labelled, showing another angular case in the same progressive series.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/242.svghttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/243.svgupper M squaredhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/244.svgupper Shttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/245.svgupper Phttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/246.svgupper X 1 upper Vhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/247.svgupper J squaredhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/248.svgj squaredhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/249.svgupper X 2 upper Vhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/250.svghttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/251.svgupper X 3 upper Vhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/252.svgupper M squaredhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/253.svgm squaredhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/254.svgupper M cubedhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/255.svgm cubedhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/i_p055.webpFourth variant of the sector diagram, rays X2, X3 upper-left and Y2, Y3 lower-right now spread wider still, approaching the horizontal CD, showing the limiting case as the parallel postulate is approached.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/i_p070.webpLines EF and CAD intersecting, with small triangle ABG formed at their crossing point, and short ray AH below, illustrating a proposition about angles formed when a line crosses another with a small angular deviation.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/256.svgupper B upper C upper Fhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/257.svgupper Xhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/258.svgupper Yhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/259.svgupper Zhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/260.svgupper A upper Hhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/i_f006.webpCharles Dodgson's postulate.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/cover.webpDodgson's 1888 witty defense of Euclidean geometry, replacing the Parallel Postulate with a simpler axiom while resisting the growing influence of non-Euclidean alternatives.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/i_f004.webpdecorativehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosa-mathematica-part-i/images/i_f007.webpTitle page of the book Curiosa Mathematica Part I written by Charles Dodgson. https://openoldbooks.com/books/curiosities-of-christian-history/read2026-11-15T15:48:14.650Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosities-of-christian-history/images/cover.webp https://openoldbooks.com/books/curiosities-of-civilization/read2026-11-15T15:48:14.650Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosities-of-civilization/images/img01.webpFig. 1https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosities-of-civilization/images/img02.webpFig. 2https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosities-of-civilization/images/img03.webpFig. 3https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosities-of-civilization/images/img04.webpFig. 4https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosities-of-civilization/images/img05.webpFig. 5https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosities-of-civilization/images/img06.webpFig. 6https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosities-of-civilization/images/img07.webpFig. 7https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosities-of-civilization/images/cover.webp https://openoldbooks.com/books/curiosities-of-great-britain-england-wales/read2026-11-15T15:48:14.650Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/curiosities-of-great-britain-england-wales/images/illus002.webptitle 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Physeterhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-creatures-in-zoology/images/i_217-a.webpThrow a tub to a whale: conciliating Physetershttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-creatures-in-zoology/images/i_217-b.webpA whale uprearing, and coming down again on an unfortunate vesselhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-creatures-in-zoology/images/i_218.webpDevil Whalehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-creatures-in-zoology/images/i_221.webpThe affection of the whale toward its younghttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-creatures-in-zoology/images/i_222.webpA whale with jaws long and full of teethhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-creatures-in-zoology/images/i_224.webpA Whale Househttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-creatures-in-zoology/images/i_226-a.webpBearded and maned 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Horsehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-creatures-in-zoology/images/i_235.webpThe Sea-Pighttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-creatures-in-zoology/images/i_236.webpThe Walrushttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-creatures-in-zoology/images/i_239.webpThe Ziphiushttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-creatures-in-zoology/images/i_244-a.webpThe Narwhalhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-creatures-in-zoology/images/i_244-b.webpA one-horned monster with a sharp nose, devouring a Gambarus.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-creatures-in-zoology/images/i_246.webpThe Swamfisckhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-creatures-in-zoology/images/i_248-a.webpFish with curious letters marked on themhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-creatures-in-zoology/images/i_248-b.webpFish ornamented with an inscription in an unknown tonguehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-creatures-in-zoology/images/i_249.webpPike marked with a cross on its side and a star on its foreheadhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-creatures-in-zoology/images/i_250.webpFish driven on shorehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-creatures-in-zoology/images/i_251.webpA rain of fisheshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-creatures-in-zoology/images/i_252.webpIll Omenhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-creatures-in-zoology/images/i_255.webpThe Dog-fishhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-creatures-in-zoology/images/i_256.webpThe Sea Dragonhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-creatures-in-zoology/images/i_257.webpThe Sting Rayhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-creatures-in-zoology/images/i_261.webpZoophytes and Spongeshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-creatures-in-zoology/images/i_262.webpPolyp seizing a sailorhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-creatures-in-zoology/images/i_263.webpThe Krakenhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-creatures-in-zoology/images/i_264.webpThe Polypushttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-creatures-in-zoology/images/i_268.webpThe Sea-Serpenthttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-creatures-in-zoology/images/i_269.webpThe Sea-Serpenthttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-creatures-in-zoology/images/i_271.webpThe Sea-Snakehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-creatures-in-zoology/images/i_272.webpA Sea Serpenthttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-creatures-in-zoology/images/i_275.webpA Sea-Serpent of extraordinary dimensionshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-creatures-in-zoology/images/i_290.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-creatures-in-zoology/images/i_292-a.webpA Serpent with seven headshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-creatures-in-zoology/images/i_292-b.webpHercules and the Hydrahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-creatures-in-zoology/images/i_293.webpFrotho kills a huge fierce great Serpent.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-creatures-in-zoology/images/i_301.webpThe Great Sea Dragonhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-creatures-in-zoology/images/i_303.webpA Dragonhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-creatures-in-zoology/images/i_307.webpThe fight of King Harald against a tame dragonhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-creatures-in-zoology/images/i_313.webpA hippopotamus eating a crocodilehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-creatures-in-zoology/images/i_317.webpthe Basiliskhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-creatures-in-zoology/images/i_318.webpthe King of Serpentshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-creatures-in-zoology/images/i_323.webpThe Salamanderhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-creatures-in-zoology/images/i_329.webpThe Leechhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-creatures-in-zoology/images/i_333-a.webpBees infesting drunkardshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-creatures-in-zoology/images/i_333-b.webpThe Hornethttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-creatures-in-zoology/images/i_334.webp https://openoldbooks.com/books/curious-epitaphs/read2026-11-15T15:48:14.650Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-epitaphs/images/symbol25.webp[symbol]https://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-epitaphs/images/img03.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-epitaphs/images/img04.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-epitaphs/images/img05.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-epitaphs/images/img06.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-epitaphs/images/img07.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-epitaphs/images/img08.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-epitaphs/images/img09.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-epitaphs/images/img10.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-epitaphs/images/img11.webpGood frend for Iesvs sake forbeare, to dicc the dvst encloased heare, Bleste be ye man yt spares thes stones, and cvrst be he yt moves my bones.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-epitaphs/images/img12.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-epitaphs/images/img13.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-epitaphs/images/img14.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-epitaphs/images/img15.webpYe Endehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-epitaphs/images/frontis.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-epitaphs/images/img01.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-epitaphs/images/img02.webp https://openoldbooks.com/books/curious-epitaphs-collected-from-the-graveyards-of-great-britain-and-ireland/read2026-11-15T15:48:14.650Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-epitaphs-collected-from-the-graveyards-of-great-britain-and-ireland/images/img01.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-epitaphs-collected-from-the-graveyards-of-great-britain-and-ireland/images/cap_a.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-epitaphs-collected-from-the-graveyards-of-great-britain-and-ireland/images/cap_t.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-epitaphs-collected-from-the-graveyards-of-great-britain-and-ireland/images/cap_m.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-epitaphs-collected-from-the-graveyards-of-great-britain-and-ireland/images/cap_s.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-epitaphs-collected-from-the-graveyards-of-great-britain-and-ireland/images/cap_w.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-epitaphs-collected-from-the-graveyards-of-great-britain-and-ireland/images/img02.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-epitaphs-collected-from-the-graveyards-of-great-britain-and-ireland/images/cap_p.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-epitaphs-collected-from-the-graveyards-of-great-britain-and-ireland/images/img03.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-epitaphs-collected-from-the-graveyards-of-great-britain-and-ireland/images/img04.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-epitaphs-collected-from-the-graveyards-of-great-britain-and-ireland/images/img05.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-epitaphs-collected-from-the-graveyards-of-great-britain-and-ireland/images/img06.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-epitaphs-collected-from-the-graveyards-of-great-britain-and-ireland/images/cover.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-epitaphs-collected-from-the-graveyards-of-great-britain-and-ireland/images/frontis.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-epitaphs-collected-from-the-graveyards-of-great-britain-and-ireland/images/title_tmb.webp https://openoldbooks.com/books/curious-facts-in-the-history-of-insects-including-spiders-and-scorpions/read2026-11-15T15:48:14.650Zmonthly0.6 https://openoldbooks.com/books/curious-if-true-strange-tales/read2026-11-15T15:48:14.650Zmonthly0.6 https://openoldbooks.com/books/curious-myths-of-the-middle-ages/read2026-11-15T15:48:14.650Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-myths-of-the-middle-ages/images/cmma02.webpRefer to captionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-myths-of-the-middle-ages/images/cmma03.webpHow to hold a divining rodhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-myths-of-the-middle-ages/images/cmma04.webpVarious ways to hold divining rodshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-myths-of-the-middle-ages/images/cmma05.webpA man carrying a bundle of stickshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-myths-of-the-middle-ages/images/cmma06.webpRepresentation of the moon in Gyffyn Churchhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-myths-of-the-middle-ages/images/cmma07.webpThe seal with the legend visiblehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-myths-of-the-middle-ages/images/cmma01.webpPope Joan on the gallows, with two demons approaching https://openoldbooks.com/books/curious-punishments-of-bygone-days/read2026-11-15T15:48:14.650Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-punishments-of-bygone-days/images/illus-010.webpLaying by the heels in the Bilboes.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-punishments-of-bygone-days/images/illus-022.webpThe Ducking-Stoolhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-punishments-of-bygone-days/images/illus-042.webpThe Stocks.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-punishments-of-bygone-days/images/illus-059.webpThe Pillory.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-punishments-of-bygone-days/images/illus-074.webpThe Burning of Bookshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-punishments-of-bygone-days/images/illus-089.webpWhipping at the Cart's Tayle.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-punishments-of-bygone-days/images/illus-107.webpThe Scarlet Letter.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-punishments-of-bygone-days/images/illus-119.webpThe Branks.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-punishments-of-bygone-days/images/illus-131.webpPublic Penancehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-punishments-of-bygone-days/images/illus-146.webpTyding the Wooden-Horsehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-punishments-of-bygone-days/images/illus-167.webpBranding.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-punishments-of-bygone-days/images/illus-002.webpThe Drunkards Cloak.https://openoldbooks.sgp1.digitaloceanspaces.com/books/curious-punishments-of-bygone-days/images/illus-004.webp https://openoldbooks.com/books/curlie-carson-listens-in/read2026-11-15T15:48:14.650Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/curlie-carson-listens-in/images/illus-emb.webpemblem https://openoldbooks.com/books/curly/read2026-11-15T15:48:14.650Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/curly/images/cover.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curly/images/tp.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curly/images/frontis.webp https://openoldbooks.com/books/curly-and-floppy-twistytail-the-funny-piggie-boys/read2026-11-15T15:48:14.650Zmonthly0.6 https://openoldbooks.com/books/curly-locks/read2026-11-15T15:48:14.650Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/curly-locks/images/0001m.webp0001mhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curly-locks/images/0003m.webp0003mhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curly-locks/images/0006m.webp0006mhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curly-locks/images/0007m.webp0007mhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curly-locks/images/0010m.webp0010mhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curly-locks/images/0012m.webp0012m https://openoldbooks.com/books/curlytops-and-their-playmates/read2026-11-15T15:48:14.650Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/curlytops-and-their-playmates/images/iad03.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curlytops-and-their-playmates/images/iad05.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curlytops-and-their-playmates/images/i002.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curlytops-and-their-playmates/images/i003.webp95https://openoldbooks.sgp1.digitaloceanspaces.com/books/curlytops-and-their-playmates/images/i001.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curlytops-and-their-playmates/images/cover.webpby Howard R. Garishttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curlytops-and-their-playmates/images/front.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curlytops-and-their-playmates/images/iad01.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curlytops-and-their-playmates/images/iad02.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curlytops-and-their-playmates/images/iad04.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/curlytops-and-their-playmates/images/iad06.webp https://openoldbooks.com/books/current-history-a-monthly-magazine-of-the-new-york-times/read2026-11-15T15:48:14.650Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i407-t.webpSENATOR J. HAMILTON LEWIShttps://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i414-t.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i418-t.webpHENRY P. DAVISON Chairman of the War Council of the American Red Cross Society (© Harris & Ewing)https://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i419-t.webpThe actual surrender of Jerusalem, Dec. 9, 1917, when two British outposts met the Mayor (carrying a cane) and his party with the white flag. The formal surrender took place next day. (© American Colony Photographers)https://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i426-t.webpWORLD'S SHIPPING LOSSES IN 1917. THE BLACK EXTENSION OF EACH COLUMN SHOWS THE GERMAN EXAGGERATION. THE AVERAGE EXAGGERATION FOR THE 12 MONTHS IS 58 PER CENT.https://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i427-t.webpWORLD'S LOSSES OF SHIPPING IN COMPARISON WITH WORLD'S TOTAL SHIP CONSTRUCTIONhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i430-t.webpSHIPPING LOSSES OF UNITED KINGDOM AS COMPARED WITH OUTPUT OF NEW SHIPShttps://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i433-t.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i448-t.webpMAP SHOWING LAGOONS AND MARSHES BETWEEN VENICE AND THE PIAVE, WHERE THE ITALIAN NAVY IS HELPING TO HOLD BACK THE INVADERShttps://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i453-t.webpONE OF THE MANY SMALL NAVAL BATTERIES THAT ARE DEFENDING VENICE IN THE NEIGHBORING LAGOONS.https://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i460-t.webpDWELLING HOUSES IN VENICE RUINED BY AIR-RAID BOMBShttps://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i552-t.webpCHART SHOWING POSITIONS IN BATTLE OF JUTLAND IN RELATION TO SURROUNDINGS OF THE NORTH SEA. (1) SCENE OF BATTLE. (2) POSITION OF BRITISH FLEET AT 3 A. M., JUNE 1, 1916, BEFORE RETRACING ITS COURSE TO THE BATTLEFIELD.https://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i559-t.webpMake-Up and Armament of British Grand Fleet In addition the Grand Fleet comprised Rear Admiral Hood's squadron of three battle cruisers and Rear Admiral Arbuthnot's squadron of four armored cruisers.https://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i590-t.webpMAP OF THE BATTLE OF CAMBRAI, SHOWING FURTHEST BRITISH ADVANCE AND GROUND LOST AFTER GERMAN ATTACK. (SEE KEY ABOVE.)https://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i610-t.webp[American Cartoon] In the Hands of His Friends —From The San Francisco Chronicle.https://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i611a-t.webp[American Cartoons] "Vorwärts Mit Gott!" Sacrificing the Manhood and Youth of a Nation to Save a Throne.https://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i611b-t.webp—From The New York Times. "Hold the line! We're coming ten million strong!"https://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i612-t.webp[Italian Cartoon] In Danger of Shipwreck —From Il 420, Florence. President Wilson's war aims threaten to bring disaster to the Central Powers' peace boat.https://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i613-t.webp[English Cartoon If They Had Been Rationed —From London Opinion. How certain great historical personages might have looked if they had lived in the days of bread cards.https://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i614-t.webp[German Cartoon] Smoking the Peace Pipe —From Der Brummer, Berlin. The Entente: "What a pity we are excluded!"https://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i615-t.webp[English Cartoon] The Rescuer's Usual Fate! —From London Opinion. Policeman John Bull: "But I only came on the scene because he had started to knock you about!" Mrs. Russia: "Never mind about that. Go on, Bill, teach 'im to interfere—hit me again."https://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i616-t.webp[American Cartoon] Proving a Fallacy —From The Chicago Herald. Russia's faith in Socialist pacifism, and what came of it.https://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i617-t.webp[English Cartoon] A Threatened Interruption —From London Opinion. ["Japan will take steps of the most decided and most adequate character to meet the occasion."—Viscount Motono, Minister for Foreign Affairs.]https://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i618-t.webp[English Cartoon] Russia's Fate —From The Passing Show, London. If he would go fooling around with him what could they do?https://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i619-t.webp[English Cartoon] Futurist Art in Russia —From The National News, London. Sturdy Old Burgess: "And what, Sir, may your picture represent?" Pluperfect Futurist Trotzky: "The mental state of a Bolshevik contemplating 'German capitalists, bankers, and landlords, supported by the silent co-operation of English and French bourgeoisie.'" Sturdy Old Burgess: "Sir, you have produced a priceless masterpiece—and if it is true that you have sold it for £22,000 you have given it away!"https://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i620a-t.webp[American Cartoons] The Wurst Is Yet to Come —San Francisco Call-Post.https://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i620b-t.webpHis New Trousers —San Francisco Call-Post.https://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i620c-t.webpThe Kaiser's God —San Francisco Chronicle.https://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i620d-t.webpTougher Than Bear Meat —San Francisco Chronicle.https://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i621a-t.webp[American Cartoons] Judging the Landslide by a Pebble —From Collier's.https://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i621b-t.webp"That's My Fight Too!" —New York World.https://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i621c-t.webpDealing With Gas Attacks —Dallas News.https://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i622-t.webp[German Cartoon] Italy's Troubles —From Der Brummer, Berlin. Italy: "Hang it all! I have been at this window for nearly three years!"https://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i623-t.webp[Dutch Cartoon] Austria and America —From De Amsterdammer, Amsterdam. German Drill Sergeant: "Now, Austrians! Eyes front! Mark time! Keep your eyes on me!"https://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i623b-t.webp[Italian Cartoon] That Dinner in Paris —From Il 420, Florence. Wilhelm: "Now that we have settled Russia, prepare that Paris feast." Chef: "For Paris, Sire? I am afraid the food will turn bad, as it did the other time."https://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i623c-t.webp[American Cartoon] The Hohenzollern Fingerprints —Macauley in Butterfield Syndicate.https://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i624a-t.webp[English Cartoon] "Here's to Dear Old Trotzky!" —Passing Show, London.https://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i624b-t.webp[American Cartoon] In the Lion's Mouth —Knickerbocker Press, Albany.https://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i624c-t.webp[French Cartoon] The Russian Campaign "Where are you running?" "To kill our General before he commits suicide." —From La Victoire, Paris.https://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i625-t.webp[American Cartoon] The Progress of Kultur —From The New York World.https://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i626a-t.webp[American Cartoons] Under His New Colonel—R. E. Morse —Bushnell for Central Press Association.]https://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i626b-t.webpA Tail of Camouflage —Bushnell for Central Press Association.https://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i626c-t.webpAnxious Moments —Bushnell for Central Press Association.https://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i626d-t.webpBut Can He Get Out? —Bushnell for Central Press Association.https://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i627a-t.webp[American Cartoons] "Sire, Ve Haf Located die Sammies!" —Baltimore American.https://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i627b-t.webpPutting All Their Punch in One Glove —Baltimore American.https://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i627c-t.webpBringing the War Home to Us —Baltimore American.https://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i627d-t.webpStuck —Baltimore American.https://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i628a-t.webp[American Cartoons] Another German Substitute —Dayton Daily News.https://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i628b-t.webpBack to Earth —St. Louis Post-Dispatch.https://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i628c-t.webpIt Shoots Further Than He Dreams —Dallas News.https://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i628d-t.webp"Whither Are We Going?" —Satterfield Syndicate.https://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i629a-t.webp[Russian Cartoons] The Bolsheviki as Art Collectors —From Novi Satirikon, Petrograd.https://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i629b-t.webpThus It Was—Thus It Is —From Novi Satirikon, Petrograd.https://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i629c-t.webpThe Bolsheviki Even Brought the English to Their Knees [Russian papers state that prayers for Russia were held in England, beginning, "Save Russia from the Bolsheviki."]https://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i629d-t.webpThe Feast —From Novi Satirikon, Petrograd.https://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i701-t.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i548-t.webpBattle of Jutland I. By Allan Westcott, U.S. Naval Academy.https://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i227-t.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i254a-t.webpGen. Sir H. S. Hornehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i254b-t.webpGen. Sir H. C. O. Plumer (Bain News Service)https://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i254c-t.webpGen. Sir Julian Byng (Underwood)https://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i254d-t.webpGen. Sir H. S. Rawlinsonhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i255a-t.webpGen. Ludendorff, Quartermaster General of the Armyhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i255b-t.webpGen. von Kathenhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i255c-t.webpGen. Otto von Below (Press Illustrating Service)https://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i255d-t.webpGen. von Gallwitzhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i291-t.webpThe United States Congress in wartime, including nearly all the members of the House, on the steps of the Capitol (© Harris & Ewing)https://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i292-t.webpAn American first aid station in the trenches in France (© Committee on Public Information)https://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i299-t.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i336-t.webpCHART OF UNITED STATES WAR DEPARTMENT'S SYSTEM OF ORGANIZATION FOR WAR ACTIVITIES.https://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i371-t.webpRepresentatives of the Central Powers at Brest-Litovsk (from left to right): Gen. Hoffmann of the German Army; Count Czernin, Austro-Hungarian Foreign Minister, Talaat Pasha, Turkish Grand Vizier, and von Kuehlmann, German Foreign Minister (International Film Service)https://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i372-t.webpPanorama of Venice as seen from an airplane in wartimehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i397-t.webpSENATOR WILLIAM E. BORAHhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i463-t.webpST. MARK'S CATHEDRAL IN WAR GARB: THE BRONZE HORSES HAVE BEEN REMOVED FROM OVER THE MAIN ENTRANCE, AND PARTS OF THE FACADE ARE PROTECTEDhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i466-t.webpINTERIOR OF ST. MARK'S: CHAPEL OF THE CRUCIFIX PROTECTED BY SANDBAGS AND MATTRESS-LIKE SHEATHShttps://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i187-t.webpPRESIDENT WILSON The first portrait of President Wilson since America entered the war, taken at the White House March 19, 1918 (© Sun Printing and Publishing Association)https://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i188-t.webpFERDINAND FOCH Generalissimo of the allied armies on the western fronthttps://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i205-t.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i206-t.webpMAP OF THE BATTLE OF PICARDY. THE CHAIN LINE ON THE EAST SHOWS BATTLE FRONT MARCH 21, 1918. SHADED SPACE INDICATES GERMAN GAINS UP TO APRIL 17. BROKEN LINE SHOWS NEW FRONT AT THAT DATE. INTERVENING LINES INDICATE GERMAN POSITIONS MARCH 24 AND 26.https://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i209-t.webpFLANDERS SECTOR OF THE GREAT BATTLE OF PICARDY. THE CHAIN LINE SHOWS BATTLEFRONT, MARCH 21, 1918. SHADED SPACE INDICATES GERMAN GAINS UP TO APRIL 17.https://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i213a-t.webpDETAIL MAP OF NORTHERN SECTOR OF BATTLE OF PICARDY, WHERE HEAVY BLOWS WERE STRUCK BY THE GERMANS IN THEIR DRIVE TOWARD AMIENS AND THE ENGLISH CHANNEL. THE FIGHTING WAS ESPECIALLY HEAVY AROUND PERONNE AND ALBERThttps://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i213b-t.webpDETAIL MAP OF SOUTHERN PORTION OF BATTLEFIELD, SHOWING LA FERE AND TERGNIER. WHERE GERMANS TRIED TO DRVE A WEDGE BETWEEN BRITISH AND FRENCH ARMIES. THE BATTLE SWEPT WESTWARD PAST ROYE AND MONTDIDIERhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i214-t.webpDETAIL MAP OF THE STRUGGLE FOR ARRAShttps://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i215-t.webpDETAIL MAP OF FLANDERS SECTOR AND BATTLE AROUND ARMENTIEREShttps://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i216-t.webpBENEDICT CROWELL Assistant Secretary of War and, during Mr. Baker's absence in Europe, Acting Secretary of War (© Harris & Ewing)https://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i217a-t.webpAMERICAN ARMY CHIEFS AND EXPERTS Maj. Gen. George O. Squier, Chief of Signal Corpshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i217b-t.webpLieut. Col. Edward A. Kreger, Judge Advocate General in France (© Harris & Ewing)https://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i217c-t.webpCol. Palmer E. Pierce, Director of Purchases for the War Department (© Harris & Ewing)https://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i217d-t.webpMaj. Gen. Evan M. Johnston, Temporary Commander at Camp Upton, N. Y. (Press Illustrating Service)https://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i507a-t.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i507b-t.webpPanoramic view of Camp Zachary Taylor, Louisville, Ky., where the 84th (National Army) Division is in training (© Caulfield & Shook)https://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i508a-t.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i508b-t.webpPanoramic view of Camp Sherman, Chillicothe, Ohio, where the 83d (National Army) Division is in training (Photo R. K. Wagner & Co.)https://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i511-t.webpPRINCE LICHNOWSKYhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i545-t.webpBattle of Jutland I. By Allan Westcott, U.S. Naval Academy.https://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i546a-t.webpGraves of American soldiers who perished in the sinking of the Tuscania, at Port Charlotte, Island of Islay, Scotland (Times Photo Service)https://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i546b-t.webpCounty volunteers of Islay firing a volley at the funeral of Tuscania victims at Kilnaughton, to the accompaniment of bagpipe lament (Times Photo Service)https://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-a-monthly-magazine-of-the-new-york-times/images/i547-t.webpOne of the many artistic posters used by the United States Government in the Third Liberty Loan campaign, April 6 to May 4, 1918 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https://openoldbooks.com/books/current-history-the-european-war-volume-i/read2026-11-15T15:48:14.650Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-the-european-war-volume-i/images/shaw_thumb.webpGEORGE BERNARD SHAWhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-the-european-war-volume-i/images/bennet_thumb.webpARNOLD BENNETT. See Page 60.https://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-the-european-war-volume-i/images/galsworthy_thumb.webpJOHN GALSWORTHY. (Photo by E.O. Hoppe.) See Page 102https://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-the-european-war-volume-i/images/kipling_thumb.webpRUDYARD KIPLING (Photo by E.O. Hoppe)See Page 106https://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-the-european-war-volume-i/images/chesterton_thumb.webpG.K. CHESTERTON. See Page 108https://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-the-european-war-volume-i/images/conandoyle_thumb.webpSIR ARTHUR CONAN DOYLE. (Photo by Arnold Genthe) See Page 132https://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-the-european-war-volume-i/images/pankhurst_thumb.webpCHRISTABEL PANKHURST. Photo (C) by Underwood & Underwood. See Page 68https://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-the-european-war-volume-i/images/barrie_thumb.webpJAMES M. BARRIE. See Page 100https://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-the-european-war-volume-i/images/signatures1_thumb.webpSignatureshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-the-european-war-volume-i/images/signatures2_thumb.webpSignatureshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-the-european-war-volume-i/images/vonharnack_thumb.webpADOLF VON HARNACK. See Page 198https://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-the-european-war-volume-i/images/niemeyer_thumb.webpTHEODORE NIEMEYER. See Page 206https://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-the-european-war-volume-i/images/thenewyorktimes.webpThe New York Timeshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-the-european-war-volume-i/images/logo.webpThe New York Times Logohttps://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-the-european-war-volume-i/images/maeterlinck_thumb.webpMAURICE MAETERLINCK. See Page 144https://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-the-european-war-volume-i/images/boutroux_thumb.webpEMILE BOUTROUX. (Photo from Bain News Service.) See Page 160https://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-the-european-war-volume-i/images/hauptmann_thumb.webpGERHART HAUPTMANN. See Page 175https://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-the-european-war-volume-i/images/fulda_thumb.webpLUDWIG FULDA. See Page 180https://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-the-european-war-volume-i/images/harrison_thumb.webpFREDERIC HARRISON. See Page 192https://openoldbooks.sgp1.digitaloceanspaces.com/books/current-history-the-european-war-volume-i/images/guyot_thumb.webpYVES GUYOT. See Page 194 https://openoldbooks.com/books/current-superstitions-edited/read2026-11-15T15:48:14.650Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/current-superstitions-edited/images/image01.webpH with downslanting crossbar https://openoldbooks.com/books/cursed/read2026-11-15T15:48:14.650Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/cursed/images/front.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cursed/images/logo.webp https://openoldbooks.com/books/cursed-be-the-treasure/read2026-11-15T15:48:14.650Zmonthly0.6 https://openoldbooks.com/books/cursed-by-a-fortune/read2026-11-15T15:48:14.650Zmonthly0.6 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sgp1.digitaloceanspaces.com/books/custis-lee-mansion-the-robert-e-lee-memorial-virginia/images/p24a.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/custis-lee-mansion-the-robert-e-lee-memorial-virginia/images/cover.webpCustis-Lee Mansion: The Robert E. Lee Memorial, Virginiahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/custis-lee-mansion-the-robert-e-lee-memorial-virginia/images/p00.webpU. S. DEPARTMENT OF THE INTERIOR: March 3, 1849https://openoldbooks.sgp1.digitaloceanspaces.com/books/custis-lee-mansion-the-robert-e-lee-memorial-virginia/images/p00a.webpLee on Travellerhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/custis-lee-mansion-the-robert-e-lee-memorial-virginia/images/p01.webpNATIONAL PARK SERVICE DEPARTMENT OF THE INTERIORhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/custis-lee-mansion-the-robert-e-lee-memorial-virginia/images/p02.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/custis-lee-mansion-the-robert-e-lee-memorial-virginia/images/p02a.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/custis-lee-mansion-the-robert-e-lee-memorial-virginia/images/p30.webpSketch of Robert E. Lee https://openoldbooks.com/books/custom-and-myth/read2026-11-15T15:48:14.650Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/custom-and-myth/images/35s.webpBull-roarerhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/custom-and-myth/images/113s.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/custom-and-myth/images/278s.webpFig. 1. An Australian Shieldhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/custom-and-myth/images/280s.webpFig. 2. Shieldshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/custom-and-myth/images/282s.webpFig. 3. Savage Ornamentationhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/custom-and-myth/images/283s.webpFig. 4. An Australian Stelehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/custom-and-myth/images/285s.webpFig 5. a, A Maori Design; b, Tattoo on a Maori’s facehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/custom-and-myth/images/287s.webpFig. 6. From a Maori’s Facehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/custom-and-myth/images/290s.webpFig. 7. Bushman Doghttps://openoldbooks.sgp1.digitaloceanspaces.com/books/custom-and-myth/images/293s.webpFig. 8. Red Indian Picture-Writing - The Legend of Manabozhohttps://openoldbooks.sgp1.digitaloceanspaces.com/books/custom-and-myth/images/295s.webpFig. 9. Bushman Wall-Paintinghttps://openoldbooks.sgp1.digitaloceanspaces.com/books/custom-and-myth/images/297s.webpFig. 10. Palælithic arthttps://openoldbooks.sgp1.digitaloceanspaces.com/books/custom-and-myth/images/299s.webpFig 12. Palæolithic art - a knife-handlehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/custom-and-myth/images/298s.webpFig. 11. Red Indian art - the Thunderbirdhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/custom-and-myth/images/300s.webpFig. 13. Eskimo Drawing - A Reindeer hunthttps://openoldbooks.sgp1.digitaloceanspaces.com/books/custom-and-myth/images/301s.webpFig. 14. Palæolithic sketch - a reindeerhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/custom-and-myth/images/303s.webpFig. 15. Archaic Greek Gems https://openoldbooks.com/books/custom-and-myth-new-edition/read2026-11-15T15:48:14.650Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/custom-and-myth-new-edition/images/cam03.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/custom-and-myth-new-edition/images/cam04.webpThree tall shieldshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/custom-and-myth-new-edition/images/cam05.webpDecorated pottery and wooden objectshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/custom-and-myth-new-edition/images/cam06.webpShowing human and animal figureshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/custom-and-myth-new-edition/images/cam07.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/custom-and-myth-new-edition/images/cam08.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/custom-and-myth-new-edition/images/cam09.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/custom-and-myth-new-edition/images/cam10.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/custom-and-myth-new-edition/images/cam11.webpDepicting four hunters with a captive beasthttps://openoldbooks.sgp1.digitaloceanspaces.com/books/custom-and-myth-new-edition/images/cam12.webpDepicting two horse-like animalshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/custom-and-myth-new-edition/images/cam13.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/custom-and-myth-new-edition/images/cam14.webpDepicting a crouching deerhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/custom-and-myth-new-edition/images/cam15.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/custom-and-myth-new-edition/images/cam16.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/custom-and-myth-new-edition/images/cam17.webpThree different ornaments depicting hunters and their preyhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/custom-and-myth-new-edition/images/cam01.webpA New Zealand bull-roarerhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/custom-and-myth-new-edition/images/cam02.webpTwo examples of scarab substitutes https://openoldbooks.com/books/customs-and-fashions-in-old-new-england/read2026-11-15T15:48:14.650Zmonthly0.6 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https://openoldbooks.com/books/cutting-it-out-how-to-get-on-the-waterwagon-and-stay-there/read2026-11-15T15:48:14.650Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/cutting-it-out-how-to-get-on-the-waterwagon-and-stay-there/images/image001.webp(cover)https://openoldbooks.sgp1.digitaloceanspaces.com/books/cutting-it-out-how-to-get-on-the-waterwagon-and-stay-there/images/image002.webp(publisher's symbol) https://openoldbooks.com/books/cuttyhunk/read2026-11-15T15:48:14.650Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/cuttyhunk/images/i003_shaft.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cuttyhunk/images/i004_gosnoldsisland.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cuttyhunk/images/i004.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cuttyhunk/images/i005_southshore.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cuttyhunk/images/i006.webpSailboats at harbor's edgehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cuttyhunk/images/i007_thevillage.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cuttyhunk/images/i008_clubhouse.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cuttyhunk/images/i008clubhousegarden.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cuttyhunk/images/i009_postoffice.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cuttyhunk/images/i010_fishermanshome.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cuttyhunk/images/i011_churchschool.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cuttyhunk/images/i011_lifesavsta.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cuttyhunk/images/i012_wreck.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cuttyhunk/images/i013_lifesavcrew.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cuttyhunk/images/i013_practice.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cuttyhunk/images/i014_glimpse.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cuttyhunk/images/015.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cuttyhunk/images/i016_vineyardsound.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cuttyhunk/images/i002.webp https://openoldbooks.com/books/cy-whittaker-s-place/read2026-11-15T15:48:14.650Zmonthly0.6 https://openoldbooks.com/books/cycle-rides-round-london/read2026-11-15T15:48:14.650Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_hr.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_x.webpList of Illustrationshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_003.webpMap—WINDSOR to SOUTHALLhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_004.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_013.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_020.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_024.webpSURBITON to LEATHERHEADhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_026.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_028.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_030.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_031.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_032.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_033.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_035.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_038.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_039.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_040.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_041.webpMap—Borough Green Statn. to Sevenoaks Statn.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_043.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_045.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_050.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_051.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_054.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_055.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_056.webpMap—ERITH to OTFORDhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_057.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_058.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_060.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_062.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_064.webpMap—BROMLEY to CROYDONhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_066.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_071.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_073.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_076.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_078.webpMap—GREENSTEAD to CHADWELL HEATHhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_079.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_081.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_083.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_088.webpMap—BRENTWOOD to Dagenham Statn.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_089.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_091.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_096.webpParslowes, Dagenham.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_098.webpEwell Old Church Towerhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_099.webpMap—EWELL to Leith Hillhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_103.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_107.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_112.webpMap—Esther Station to Byfleet Stationhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_113.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_119.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_122.webpMap—EDGEWARE to PINNERhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_123.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_127.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_128.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_132.webpMap—FARNHAM to ALBURYhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_133.webpMap—SHERE to REDHILLhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_134.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_136.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_137.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_139.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_141.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_143.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_151.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_156.webpMap—BRACKNELL to Esher Stationhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_157.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_160.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_164.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_170.webpMap—Kingston to Croydonhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_173.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_175.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_179.webpMap—Ewell Station to Lingfield Stationhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_180.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_181.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_183.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_184.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_187.webpMap—WESTERHAM to TONBRIDGEhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_189.webpThe Gatehouse, Hever Castle.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_191.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_195.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_196.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_197.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_198.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_200.webpMap—EGHAM to HOUNSLOWhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_205.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_208.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_211.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_218.webpMap—DARTFORD to Borough Green Statn.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_219.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_220.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_221.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_225.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_232.webpMap—HERTFORD to WALTHAM ABBEYhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_233.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_235.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_236.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_237.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_242.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_245.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_247.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_251.webpMap—Westminster Bridge to Brightonhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_253.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_255.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_258.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_261.webpMap—BARKING to CHATHAMhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_263.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_267.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_269.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_271.webpLeigh Marshes and the Mouth of the Thames.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_277.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_283.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_285.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_288.webpThe Endhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_frontis.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycle-rides-round-london/images/i_title.webpCyclist https://openoldbooks.com/books/cycling-and-shooting-knickerbocker-stockings-how-to-knit-them-with-plain-and-fan/read2026-11-15T15:48:14.650Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/cycling-and-shooting-knickerbocker-stockings-how-to-knit-them-with-plain-and-fan/images/logo.webpPrinter's Logohttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycling-and-shooting-knickerbocker-stockings-how-to-knit-them-with-plain-and-fan/images/sock_tn.webpSockhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cycling-and-shooting-knickerbocker-stockings-how-to-knit-them-with-plain-and-fan/images/i07.webpFancy Top No. 1https://openoldbooks.sgp1.digitaloceanspaces.com/books/cycling-and-shooting-knickerbocker-stockings-how-to-knit-them-with-plain-and-fan/images/i15.webpStocking No. 2https://openoldbooks.sgp1.digitaloceanspaces.com/books/cycling-and-shooting-knickerbocker-stockings-how-to-knit-them-with-plain-and-fan/images/i22.webpFancy Top No. 3https://openoldbooks.sgp1.digitaloceanspaces.com/books/cycling-and-shooting-knickerbocker-stockings-how-to-knit-them-with-plain-and-fan/images/i23.webpFancy Top No. 4https://openoldbooks.sgp1.digitaloceanspaces.com/books/cycling-and-shooting-knickerbocker-stockings-how-to-knit-them-with-plain-and-fan/images/i25.webpStocking Top No. 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https://openoldbooks.com/books/cyclopedia-of-painters-and-paintings-vol-2/read2026-11-15T15:48:14.650Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/colophon.webpScribner's colophonhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_055a.webpSignature: C. F.ciushttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_055b.webpBust of Faccini, chest facing slightly left, looking forward; mustache, goatee, and short hair.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_055c.webpBust of Thomas Faed, facing right. Full beard and mustache, short curly hair.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_057.webpInitials and signature: A F. A f falconehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_058.webpSignature: V Falenshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_059.webpAbstract designs resembling flowers or cumulus clouds.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_060a.webpSignature: Fasola Da Pavia 1560https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_060b.webpBust of Il Fattore, facing slightly right; full beard and mustache; wears a striped turban.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_062.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_063.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_064.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_065.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_069a.webpBust of Ferrari, facing slightly right; curled mustache, small goatee, curly hair to his shoulders.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_069b.webpBust of Ferri facing forward; thin mustache, long curly locks below his shoulders (wig?)https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_069c.webpSignature: G. FERRIER ROME 1874https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_070a.webpSignature: M. Feselenhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_070b.webpBust of Feti, facing forward; clean shaven, wavy hair to his shoulders, parted in the middle.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_070c.webpSignature: D. Fetihttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_070d.webpBust of Feuerbach, facing left. Handlebar mustache, small goatee; wavy hair brushed away from the face.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_071a.webpBust of Feyen-Perrin, facing right; full mustache and beard; wavy hair to the nape, parted in the center.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_071b.webpInitials: O.F.F. 1565https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_071c.webpIntertwined intials: FO, OFhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_073.webpBust of Fildes, facing right; beard and mustache, with trimmed slightly wavy hairhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_074.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_076.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_078.webpBust of Flameng, facing slightly left; sports a full handlebar mustache; short hair.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_079.webpBust of Flandrin, facing right. Full beard and mustache, thinnning hair at forehead; hair clipped to nape.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_080.webpSignature: B. Flemaelhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_082a.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_082b.webpBust of Flinck, facing forward; thin mustache, small goatee; wavy hair to shoulders.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_083a.webpTwo signatures: G Flinck anjd Flinck G 1646https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_083b.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_084.webpBust of Floris, facing forward; beard, mustache, and short hair.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_086a.webpBust of Fontana, facing left, gazing forward; cap over her hair and high ruff around neck.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_086b.webpSignatures: Lav. Fon. Prse., LAVINIA PROSPERI FONTANAE FAC.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_088.webpBust of Forest, looking slightly left. Clean-shaven, wearling a large turban.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_089a.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_089b.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_090a.webpBust of Förster, facing slightly right. Mustache, mutton chops, hair combed away from face.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_090b.webpInterlocked initials: FF 828https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_091.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_092.webpBust of Fortuny y Carbó, facing forward; mustache and small goatee; short, curly hair.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_093.webpSignature: Fortuny 74https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_094.webpBust of Fouquières, facing forward; scruffy beard and mustache; wavy hair to the shoulders.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_095a.webpBust of Fragonard, facing forward; clean shaven, short hair. High collar to the chin.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_095b.webpTwo signatures: HFragonard, Fragonard 1775https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_095c.webpBust of Francais, facing slightly right; full beard and mustache; short hairhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_096.webpBust of Francesca, facing slightly right; clean shaven, short curly hair, wearing a cap.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_097.webpBust of Franceschini, facing forward; thin mustache, curly hair to shoulders, wearing a soft hat.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_099a.webpBust of Francia, facing slightly right; clean shaven, short wavy hair, wearing a soft cap.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_099b.webpSignature: Francia Aurifaber Bono.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_099c.webpSignature: I FRANCIAhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_101a.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_101b.webp3 sets of interlocking initials, each with 3 letters, F; below two are the years 1685 and 1683.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_102a.webpConnected initials: AF.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_102b.webpBust of Francken, facing forward. Has a full beard and mustache, short curly hair.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_103.webpSignatures: F Francken, Aᵒ 1615, F Franckenhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_104.webpBust of H. Francken, facing slightly right, looking forward; mustache, goatee, stubble along bottom of chin; curly hair; wears a gathered ruff.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_105.webpSignature: franquelin 1830https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_106.webpSignature: fraser.Ahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_107a.webpBust of Fréminet, facing slightly left; mustache and full goatee, curly hair; wears a high collar up to his chin.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_107b.webpConnected initials, MFre, and printed name, FREMINEThttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_108a.webpBust of Frère, facing slightly left; full beard and mustache, receding hairline, wavy hair.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_108b.webpSignature: Edouard Frère, 85.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_110.webpIntertwined intials: EF.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_111a.webpBust of Frith, facing slightly right; mutton chops, heavy eyebrows, wavy hair.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_111b.webpBust of Frölich, facing slightly left, gazing forward; full beard and mustache; wearing a hat with a brim.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_112.webpBust of Fromentin, facng slightly right; full beard and mustache, receding hairline.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_113a.webpSignature: Eug. Fromentinghttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_113b.webpBust of Frost, facing forward; long sideburns, thick wavy hair.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_115a.webpBust of Führich, facing slightly right; clean shaven, wearing wire-rim glasses; short wavy hair.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_115b.webpBust of Fuller, facing slightly right; full beard and mustache, wavy hair.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_116.webpSignatue: furinihttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_117.webpBust of Fuseli, facing slightly left, left hand raised to side of face; thick curly hairhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_118a.webpInitials and Signature: J. Fy and Joh. Fyt. 1650https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_118b.webpBust of Gabbiani, facing right, looking forward; clean shaven, long wavy hair to mid-chest.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_119a.webpSignature: G Gabron 1670https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_119b.webpBust of Gaddi, facing right; pointed beard, wearing a turbanhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_120a.webpSignature: T Gaddi fecithttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_120b.webpInitials: B.G. and B Ghttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_120c.webpSignature: A / Gaelen 1719https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_121.webpBust of Gainsborough, looking forward; clean shaven, wavy hair parted in the center.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_122.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_123.webpBust of Gallait, facing left; beard, mustache; slightly receding hairline; short hair.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_124.webpSignature: Galloche 1752https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_125a.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_125b.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_126.webpBust of Garbo, looking downward to right; clean shaving, curly hair to shoulders, wearing a cap.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_128.webpSignature: B. Garofolohttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_129a.webpInterlocked initials: GLhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_129b.webpSignature: Gassies 1820https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_130.webpSignature: L P Gaudin 1618https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_131.webpSignatures: L. Gauffier 1789 and L. Gauffier Rome 1792https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_133a.webpBust of Gebhardt, facing right. Long full beard and mustache, receding hairline, long hair to shoulders.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_133b.webpPair of connected initials: AGhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_134.webpSignature: Van Geel Fecithttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_135.webpBust of Geertz, facing slightly right; full mustache and beard, short hair brushed away from face.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_138.webpBust of Genelli, facing slightligh right. Full beard, long mustache, receding hairline, wavy hair.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_139a.webpBust of Genoels, facing forward; thin mustache, long curly locks, possibly a wig.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_139b.webpIntertwined initials: AGhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_140a.webpBust of Gentileschi,facing forward; mustache and goatee, wavy hair; wearing a high collar extending to chin and ears.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_140b.webpSignatures. script: Horatius Gentleschi Florentinus f; printed: HORATIUS GENTILESCHUS. FECIT.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_142a.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_142b.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_143a.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_143b.webpBust OF Gérard, facing slightly right; clean shaven, thinning hair.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_144a.webpSignature: Bron Gérardhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_144b.webpBust of Géricault, facing forward; thin mustache, scruffy beard, short hair, wearing a cap with a feather.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_145a.webpSignature: J. Gericaulthttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_145b.webpBust of Gérôme, facing slightly right. Handlebar mustache, wavy hair cropped to the ears.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_146.webpSignature printed: J. L GEROMEhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_147a.webpBust of Gervex, facing slightly right. Trimmed beard and mustache, short hair.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_147b.webpBust of Geselschap, facing forward; long beard and mustache, wearing a brimmed hat with a ribbon around the crown.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_149.webpBust of Ghirlandajo, facing slightly left; clean shaven, wavy hair to his shoulders.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_150.webpBust of Ghirlandajo, facing slightly left; thin mustache, straight hair to his shoulders.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_152.webpBust of Gifford, facing left; long full beard and mustache, straight hair trimmed to nape and ears.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_153.webpBust of Gifford, facing forward; beard and mustache; short hair, curly around the ears.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_154.webpBust of Gilbert, facing slightly right; long full beard and mustache, curly hair, wearing a soft cap covering most of his head.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_155a.webpBust of Gillot, facing forward. Clean shaven, short wavy hair.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_155b.webpSignatures: CGillot and C Gillot 1710.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_155c.webpSignature: h Gimignani 1671https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_156.webpBust of Giordano, facing slightly left; trimmed beard and mustache; long wavy hair below the shoulders.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_157a.webpSignatures: L. Giordano and L. Giroano 1698https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_157b.webpBust of Giorgione, facing forward; full beard and mustache, short wavy hair.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_158.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_157c.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_159.webpBust of Giotto. 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V. 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Hinckel 1801https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_274b.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_274a.webpBust of Hildebrandt, facing slightly left; long mustache, short beard, hair brushed away from face.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_275a.webpBust of Hildbrandt, facing slightly left; long thick mustache, trimmed beard; hair trimmed to the ears.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_275b.webpInitials: TH TH 18266 EH 1824https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_276a.webpBust of Hill, facing forward; long beard and mustache, short curly hair.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_276b.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_279.webpBust of Hire, facing forward, looking slightly downward; thin mustache, short curly hair.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_280a.webpSignature: Meyndert Hobbema 1667https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_280b.webpSignature: M Hobbemahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_281.webpBust of Hodgson, facing slightly right; full beard and long mustache; straight hair clipped to his ears.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_282.webpSignature: J. Hoeck 1644https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_283.webpPrinted signature: G. Hoet.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_284.webpBust of Hoff, facing slightly right; thick mustache, no beard; short wavy hair.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_285.webpBust of Hogarth, facing slightly right; clean shaven, wearing a soft cap over his head.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_286a.webpInitials: W. M.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_286b.webpBust of Hoguet, facing forward; long handlebar mustache; short wavy hair.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_287a.webpBust of Holbein, facing slightly right; long mustache and beard to mid-chest; long wavy hair below the shoulders.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_287b.webpBust of Holbein, facing slightly left. 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D. Hundekueter, M. D. Hondecoeterhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_304a.webpLinked initials: AHhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_304b.webpBust of Honthorst, facing forward; mustache and goatee, curly locks to the shoulders.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_305a.webpPrinted: G HonDHORST; Script: GHonthorsthttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_305b.webpInitials: GHhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_306b.webpBust of De Hooch, facing forward; clean shaven with long hair to his shoulders.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_306a.webpInitials: DH, PD.H, P. D. Hoogh; Signature: P DHoochhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_306c.webpBust of Hoogstraten, facing forward; thin mustache and goatee; long wavy hair below shoulders.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_306d.webpInterlocked initials: SvH, SvHhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_306e.webpBust of Hook, facing slightly left; full beard and mustach, wavy hair.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_308.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_309.webpSignatures J Horemans. 1712; J Horemans f. 1738https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_310.webpBust of Horschelt, facing slightly right; thick mustache and mutton chops; short hair.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_311a.webpBust of Horsley, facing forward, hand on his cheek. Mutton chops, short hair.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_311b.webpBust of Hosemann, facing slightly left; full beard and long mustache; receding hairline.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_312a.webpSignature: M A Houcisse 1720https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_312b.webpBust of Houbraken, facing forward; clean shaven, wearing a curly wig to below the shoulders.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_312c.webpInitials: AHhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_314.webpBust of Howard, facing left; clean shaven, short hair.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_315a.webpBust of Huber, facing forward; clean shaven, wearing a soft cloth hat.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_315b.webpSignature: Rudolphe Huber 1724https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_316a.webpBust of Hübner, facing slightly right; long full mustache and beard; short hair.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_316b.webpBust of Hübner, facing forward; full mustache and beard, short hair.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_317a.webpSignature: Hudsonhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_317b.webpSignatures: J F hue 1819, and J F Hue 1787https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_317c.webpBust of Huet, facing slightly left; clean shaven, slightly wavy hair.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_318.webpSignautre: Hüet p. 1769https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_319.webpSignature: J V. Hugtenburghttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_321.webpBust of Humbert, facing forward; trimmed mustache and beard, short hair.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_322.webpBust of Hunt, facing forward; mustache and full beard; wavy hair parted in the center.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_323a.webpBust of Hunt, facing slightly right; full mustache and long beard; bald on top; short hair on the sideshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_323b.webpBust of Hünten, facing forward; full mustache, receding hairline, short hairhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_324a.webpBust of Hunter, facing forward; long mustache and mutton chops; wire-rim glasses, short hair.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_324b.webpBust of Huntington, facing right; full mustache and beard, wavy hair cut to nape.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_325.webpSignature: C Hutin 1763https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_326a.webpBust of Huysmans, facing slightly right; clean shaven, shoulder length wavy hair.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_326b.webpBust of Huysum, facing slightly right; clean shaven, wearing a long curly wig.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_327.webpSignatures: Jan Van Huysum, Jan V Huysum 1724https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_328.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_330.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_332.webpBust of Ingres, facing slightly left; clean shaven, straight hair.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_333a.webpSignature: Ingres J. 1617; printed: INGRES RoA 1618.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_333b.webpBust of Inman, facing slightly left; clean shaven, thick wavy hair.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_334b.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_334a.webpBust of Inness, facing right; mustache and beard, wire-rim glasses, long wavy hair.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_337.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_338a.webpBust of Isabey, facing slightly left; muttonchops, bald pate, wavy hair.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_338b.webpSignature: J Isabey 1817https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_338c.webpBust of Israels: facing left; full mustache and beard, side whiskers, wire-rim glasses, wavy hair.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_339.webpSignature: Jos/Israels.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_340.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_341.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_342.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_344.webpBust of Jacque, facing slightly left; mustache, wavy hair.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_345a.webpSignature: ch. Jacquehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_345b.webpBust of Jacquemart, facing forward; right hand on her chin; hair bound at the top with flowers and a veil.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_346.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_350.webpSignature: v h Janssens 1730https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_351.webpBust of Jardin, facing slightly left; thin mustache, curly locks below the shoulders, wearing a wide-brimmed hat.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_352.webpSignatures: J. Jur-f 1653; J. Jur. fe. 1646.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_353a.webpust of Jeaurat, facing forward, clean-shaven, double chin; curly hair to below the shoulders.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_353b.webpTwo signatures: E Seccurathttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_355a.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_355b.webpBust of Jerichau-Baumann, facing right; wavy hair to her shoulders, covered by a long cap.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_356.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_357.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_358.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_360.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_361.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_362.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_363.webpBust of Joest, facing slight left; clean shaven, stringy hair to his shoulders; wears a cloth cap.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_364.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_365.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_366.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_367.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_368.webpBust of Johnson, facing slighly left; long mustache, goatee; wire-rim glasses; short hair.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_370a.webpSignatures: Ludof de Junge 1690, L D Jonge.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_370b.webpBust of Jonghe, facing forward; thin mustache and goatee; wire-rim glasses; thinning hair parted in the center.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_371.webpBust of Jordaens, facing forward; handlebar mustache, goatee; wavy hair to shoulders.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_372a.webpSignatures: J Jur-f 1653; J. Jur. fe. 1646https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_372b.webpBust of Jordan, facing forward; thick mustache, thin goatee; short wavy hair.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_373.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_374.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_375.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_376.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_377.webpSignatures: J. Jouvenet pinxit 1707; Jouvenet pin 1689https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_378.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_379a.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_379b.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_380.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_381.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_384a.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_384b.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_385.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_386.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_387a.webpBust of Kaemmerer, facing forward; mustache and short beard; short hair.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_387b.webpPrinted signature: F.H.KAEMMERERhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_388a.webpBust of Kalckreuth, facing right; full mustache and beard; hair swept away from his face.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_388b.webpBust of Kalf, facing forward; clean shaven with long curly locks extending past the shouldershttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_389a.webpPrinted signature: W. KALF 1663https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_389b.webpBust of Kalkar, facing slightly right; clean shaven, curly hair, wearing a cloth hat.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_391.webpBust of Karger, facing forward; full mustache and beard; thick hair brushed away from the face.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_392.webpBust of Kauffman, looking slightly left; long locks curl beyond her shoulderhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_393a.webpInitials: A K. fecithttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_393b.webpBust of Kauffmann, facing forward; very thick, long mustache that covers a full beard; short hair.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_394a.webpBust of Kauffmann, facing slightly left; wide thin mustache; short wavy hair.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_394b.webpBust of Kaulbach, facing forward; long French beard with sideburns, long mustache; thick wavy hairhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_394c.webpBust of Kaulbach, facing slightly right; thin mustache and sideburns; thick hair.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_395a.webpBust of Kaulbach, facing forward; thick trimmed beard and flowing mustache; thick hair brushed away from frce.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_395b.webpBust of Kaulbach, facing left; thick mustache; long straight hair to collar.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_396a.webpInitials: A. K. 1631https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_396b.webpBust of Keller, facing slightly right; thick handlebar mustache; hair brushed away from face, parted in center.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_397a.webpBust of Keller, facing right; thick long mustache and French beard; straight hair swept away from face.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_397b.webpBust of Kensett, facing forward; thick long mustache intermingled with beard; short wavy hair.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_399a.webpSignature: F. V Kessel 1691https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_399b.webpBust of Kessel, facing slightly left; thin mustache and goatee; long wavy hair extending beyond shoulders.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_399c.webpSignature: J. V. Kessel 1670https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_400.webpBust of Ketel, facing forward, chest facing right; long mustache and sideburns, wavy hair; wears a ruff.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_401.webpBust of Keyser, facing slightly left; trimmed beard and mustache, straight hair trimmed to nape.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_402.webpThree interlocked initials: TDK.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_405.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_406a.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_406b.webpPrinted signature; interlocked JAK lein.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_407.webpBust of Klöcker, facing slightly right; thin mustache, long curly wig extending to mid-chest.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_408a.webpPrinted signature: AKloeber 1839https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_408b.webpSignatures: a Klomp fecit 1628; A Klomphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_409.webpBust of Knaus, facing right; full mustache and beard; straight hair clipped to nape.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_410a.webpPrinted signature: L Knaus. 1858https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_410b.webpBust of Kneller, facing slightly left; clean shaven; long curly wig extending to ches.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_411a.webpSignature: Kneller 1720https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_411b.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_412.webpBust of Knille, facing left; mustache, beard and sideburns; straight hair trimmed to nape.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_416.webpBust of Koch, facing slightly right; clean shaven, wearing a cloth cap covering most of his hair.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_417.webpInterlocked initials: BCK; script: BCK.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_421a.webpBust of Koninck, facing slightly right; very small mustache and goatee; long wavy hair extending beyond shoulders.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_421b.webpSignature: P- Koninck 1646https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_421c.webpSignature: S. Koninck A<span class="sup">o</span> 1643.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_423.webpBust of Kotzebue, facing forward; long handlebar mustache, short hair.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_425a.webpBust of Kraus, facing slightly right; thick mustache and trimmed beard; short hairhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_425b.webpBust of Kreling, facing slightly right; long mustache and trimmed beard, wearing a brimmed hat.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_428.webpBust of Kröyer, facing slightly right; long mustache and full beard; wearing lorgnette.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_429.webpBust of Krüger, facing forward; muttonchops, no beard or mustache; receding hairline, thin hair.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_430.webpBust of Küchler, facing forward; clean shaven, short hair under a cap, wearing a cowl.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_431.webpInterlocked initials: HK; above in hand-drawn box, 1511.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_433.webpPrinted signature: J Kupetzky 1713https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_434.webpBust of Kurzbauer, facing slightly right; thick mustache, sideburns, and French beard; thick hair brushed away from face.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_435.webpBust of Kyhn, facing forward; full mustache and beard; wavy hairhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_018.webpBust of Eastlake, facing slightly left, mutton chops, whispy hair, balding on top.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_020.webpIntertwined initials A Ehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_021.webpOutlined and intertwined initials C E; solid spaced initials C E.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_023.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_025.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_026.webpBust of Eeckhout, faces forward; thin mustache, wavy hair parted in the center.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_027.webpSignature: G V. Eeckouthttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_029.webpFour examples of intertwined A E initials.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_031.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_032.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_033a.webpIntertwined initials M A Ehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_033b.webpSignature: Elligerhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_033c.webpBust of Elliott, facing slightly left; wavy hair to his shoulders, full beard and mustache, receding hair at forehead.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_033d.webpBust of Elmore, facing forward, full beard and mustache, wavy hair.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_034.webpBust of Elsheimer, facing forward; full mustache, goatee, wavy hair.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_035a.webpInitials Æ and signature AElseimerhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_035b.webpSignature: Empolihttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_037a.webpFigures resembling cuneiform imageshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_037b.webpBust of Engerth, facing forward; beard, sideburns, mustache, receding hairline.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_037c.webpBust of Enhuber, facing slightly left, looking forward; thick mustache, receding hairline.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_038a.webpInitials: K.v.E. and KvE.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_038b.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_038c.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_039.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_040.webpBust of Erdmann, facing slightly left; full beard and mustache.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_041a.webpInitials: iv·ES.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_041b.webpSignature: Escalentehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_043a.webpSignature: h. j. Espinosa 1670https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_043b.webpSignature: B.Estensehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_044.webpBust of Ett, facing right, gazing downward; clean-shaven, wavy hair.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_046.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_047a.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_047b.webpBust of Everdingen, facing slightly left, gazing forward; short mustache, wavy hair to his shoulders.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_048a.webpJoined initials: AV Abhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_048b.webpIntertwined initials: CVE 1652.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_048c.webpInitials: AE joined, N. v. E., and intertwined AvEhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_049a.webpBust of Exner, facing slightly left; full mustache and beard, high foreheadhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_049b.webpBust of Eyck, facing slightly left; clean shaven, wearing a tall 14th C. style fur hat.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_050.webpBust of van Eyck, facing slightly right; clean-shaven, wearing a broad feather cap and spectacles without arms on his nose.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_051.webpIntertwined initials: JVE 1440.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-painters-and-paintings-vol-2/images/i_052.webp https://openoldbooks.com/books/cyclopedia-of-philosophy/read2026-11-15T15:48:14.650Zmonthly0.6 https://openoldbooks.com/books/cyclopedia-of-telegraphy-and-telephony/read2026-11-15T15:48:14.650Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/deco3.webpdecorativehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/deco2.webpdecorativehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/desk.webpman at deskhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig001_t.webpIllustration: Fig. 1. Type of Magneto Telephonehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig002_t.webpIllustration: Fig. 2. Magneto Telephones and Linehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig003_t.webpIllustration: Fig. 3. Magneto Telephones without Permanent Magnetshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig004_t.webpIllustration: Fig. 4. Reis Transmitterhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig005_t.webpIllustration: Fig. 5. Typical Telegraph Linehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig006_t.webpIllustration: Fig. 6. Telegraph Equipment Converted into Telephone Equipmenthttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig007_t.webpIllustration: Fig. 7. Electrostatic Telephonehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig008_t.webpIllustration: Fig. 8. Hughes' Microphonehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig009_t.webpIllustration: Fig. 9. General Types of Transmittershttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig010_t.webpIllustration: Fig. 10. Battery in Line Circuithttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig011_t.webpIllustration: Fig. 11. Battery in Local Circuithttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig012_t.webpIllustration: Fig. 12. Conventional Diagram of Talking Circuithttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig013_t.webpIllustration: Fig. 13. Induction-Coil Actionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig014_t.webpIllustration: Fig. 14. Oscillogram of Telephone Currentshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig015_t.webpIllustration: Fig. 15. Telegraph Sounder and Keyhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig016_t.webpIllustration: Fig. 16. Vibrating Bellhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig017_t.webpIllustration: Fig. 17. Elemental Magneto-Generatorhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig018_t.webpIllustration: Fig. 18. Extension of a Permanent Magnethttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig019_t.webpIllustration: Fig. 19. Extension of a Permanent Magnethttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig020_t.webpIllustration: Fig. 20. Electromagnethttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig021_t.webpIllustration: Fig. 21. Polarized Ringerhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig022_t.webpIllustration: Fig. 22. Gravity-Drophttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig023_t.webpIllustration: Fig. 23. Electromagnetic Visible Signalhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig024_t.webpIllustration: Fig. 24. Lamp Signal and Lenshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig025_t.webpIllustration: Fig. 25. Lamp Signal Controlled by Relayhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig026_t.webpIllustration: Fig. 26. Lamp Signal Directly in Linehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig027_t.webpIllustration: Fig. 27. Lamp Signal and Ballasthttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig028_t.webpIllustration: Fig. 28. Simple Condenserhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig029_t.webpIllustration: Fig. 29. Condenser Symbolshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig030_t.webpIllustration: Fig. 30. Line with Shunt Capacityhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig031_t.webpIllustration: Fig. 31. Test of Line with Varying Shunt Capacityhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig032_t.webpIllustration: Fig. 32. Spiral of Wirehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig033_t.webpIllustration: Fig. 33. Spiral of Wire Around Iron Corehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig034_t.webpIllustration: Fig. 34. Test of Line with Varying Serial Inductancehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/p56eq1.webpEquation: Z = [sqrt](R^2 + (1/C^2[omega]^2))https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/p56eq2.webpEquation: Z = [sqrt](R^2 + L^2[omega]^2)https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig035_t.webpIllustration: Fig. 35. Loaded Linehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/p60eq1.webpEquation for ahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig036_t.webpIllustration: Fig. 36. Shreeve Repeater and Circuithttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig037_t.webpIllustration: Fig. 37. Mercury-Arc Telephone Relayhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig038_t.webpIllustration: Fig. 38. Blake Transmitterhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig039_t.webpIllustration: Fig. 39. Multiple-Electrode Transmitterhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig040_t.webpIllustration: Fig. 40. White Solid-Back Transmitterhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig041_t.webpIllustration: Fig. 41. White Solid-Back Transmitterhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig042_t.webpIllustration: Fig. 42. New Western Electric Transmitterhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig043_t.webpIllustration: Fig. 43. Kellogg Transmitterhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig044_t.webpIllustration: Fig. 44. Automatic Electric Company Transmitterhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig045_t.webpIllustration: Fig. 45. Monarch Transmitterhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig046_t.webpIllustration: Fig. 46. Acousticon Transmitterhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig047_t.webpIllustration: Fig. 47. Switchboard Transmitterhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig048_t.webpIllustration: Fig. 48. Transmitter Symbolshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/frontis.webpALEXANDER GRAHAM BELL The Inventor of the Telephone.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig049_t.webpIllustration: Fig. 49. Single-Pole Receiverhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig050_t.webpIllustration: Fig. 50. Western Electric Receiverhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig051_t.webpIllustration: Fig. 51. Kellogg Receiverhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig052_t.webpIllustration: Fig. 52. Automatic Electric Company Direct-Current Receiverhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig053_t.webpIllustration: Fig. 53. Automatic Electric Company Direct-Current Receiverhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig054_t.webpIllustration: Fig. 54. Monarch Direct-Current Receiverhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig055_t.webpIllustration: Fig. 55. Dean Steel Shell Receiverhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig056_t.webpIllustration: Fig. 56. Working Parts of Dean Receiverhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig057_t.webpIllustration: Fig. 57. Operator's Receiverhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig058_t.webpIllustration: Fig. 58. Operator's Receiver and Cordhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig059_t.webpIllustration: Fig. 59. Receiver Symbolshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig060_t.webpIllustration: Fig. 60. Simple Voltaic Cellhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig061_t.webpIllustration: Fig. 61. LeClanché Cellhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig062_t.webpIllustration: Fig. 62. Carbon Cylinder LeClanché Cellhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig063_t.webpIllustration: Fig. 63. Dry Cellhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig064_t.webpIllustration: Fig. 64. Gravity Cellhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig065_t.webpIllustration: Fig. 65. Fuller Cellhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig066_t.webpIllustration: Fig. 66. Chloride of Silver Cellhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig067_t.webpIllustration: Fig. 67. Battery Symbolshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig068_t.webpIllustration: Fig. 68. Principles of Magneto Generatorhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig069_t.webpIllustration: Fig. 69. Generator Armaturehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig070_t.webpIllustration: Fig. 70. Generator Armaturehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig071_t.webpIllustration: Fig. 71. Generator Field and Armaturehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig072_t.webpIllustration: Fig. 72. Generator with Magnets Removedhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig073_t.webpIllustration: Fig. 73. Five-Bar Generatorhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig074_t.webpIllustration: Fig. 74. Generator Shunt Switchhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig075_t.webpIllustration: Fig. 75. Generator Cut-in Switchhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig076_t.webpIllustration: Fig. 76. Generator Cut-in Switchhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig077_t.webpIllustration: Fig. 77. Pulsating-Current Commutatorhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig078_t.webpIllustration: Fig. 78. Generator Symbolshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig079_t.webpIllustration: Fig. 79. Polarized Bellhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig080_t.webpIllustration: Fig. 80. Polarized Bellhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig081_t.webpIllustration: Fig. 81. Biased Bellhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig082_t.webpIllustration: Fig. 82. Ringer Symbolshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig083_t.webpIllustration: Fig. 83. Long Lever Hook Switchhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig084_t.webpIllustration: Fig. 84. Short Lever Hook Switchhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig085_t.webpIllustration: Fig. 85. Removable Lever Hook Switchhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig086_t.webpIllustration: Fig. 86. Desk-Stand Lever Hook Switchhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig087_t.webpIllustration: Fig. 87. Desk-Stand Lever Hook Switchhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig088_t.webpIllustration: Fig. 88. Hook Switch Symbolshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig089_t.webpIllustration: Fig. 89. Magnetization Curvehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig090_t.webpIllustration: Fig. 90. Bar Electromagnethttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig091_t.webpIllustration: Fig. 91. Bar Electromagnethttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig092_t.webpIllustration: Fig. 92. Horseshoe Electromagnethttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig093_t.webpIllustration: Fig. 93. Horseshoe Electromagnethttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig094_t.webpIllustration: Fig. 94. Iron-Clad Electromagnethttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig095_t.webpIllustration: Fig. 95. Electromagnet of Relayhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig096_t.webpIllustration: Fig. 96. Parallel Differential Electromagnethttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig097_t.webpIllustration: Fig. 97. Tandem Differential Electromagnethttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig098_t.webpIllustration: Fig. 98 Construction of Electromagnethttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig099_t.webpIllustration: Fig. 99. Electromagnet with Bare Wirehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig100_t.webpIllustration: Fig. 100. Electromagnet with Terminalshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig101_t.webpIllustration: Fig. 101. Section of Open-Circuit Impedance Coilhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig102_t.webpIllustration: Fig. 102. Open-Circuit Impedance Coilhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig103_t.webpIllustration: Fig. 103. Closed-Circuit Impedance Coilhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig104_t.webpIllustration: Fig. 104. Symbol of Toroidal Impedance Coilhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig105_t.webpIllustration: Fig. 105. Toroidal Impedance Coilhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig106_t.webpIllustration: Fig. 106. Symbol of Impedance Coilhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig107_t.webpIllustration: Fig. 107. Induction Coilhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig108_t.webpIllustration: Fig. 108. Section of Induction Coilhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig109_t.webpIllustration: Fig. 109. Repeating Coilhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig110_t.webpIllustration: Fig. 110. Repeating Coilhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig111_t.webpIllustration: Fig. 111. Repeating Coilhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig112_t.webpIllustration: Fig. 112. Diagram of Toroidal Repeating Coilhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig113_t.webpIllustration: Fig. 113. Toroidal Repeating Coilhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig114_t.webpIllustration: Fig. 114. Symbol of Induction Coilhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig115_t.webpIllustration: Fig. 115. Repeating-Coil Symbolshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig116_t.webpIllustration: Fig. 116. Symbol of Four-Winding Repeating Coilhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig117_t.webpIllustration: Fig. 117. Mica Card Resistancehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig118_t.webpIllustration: Fig. 118. Iron-Wire Ballasthttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig119_t.webpIllustration: Fig. 119. Condenser Platehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig120_t.webpIllustration: Fig. 120. Theory of Condenserhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig121_t.webpIllustration: Fig. 121. Rolled Condenserhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig122_t.webpIllustration: Fig. 122. Rolled Condenserhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig123_t.webpIllustration: Fig. 123. Rolled Condenserhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig124_t.webpIllustration: Fig. 124. Condenser Symbolshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig125_t.webpIllustration: Fig. 125. Local-Battery Stations with Grounded Circuithttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig126_t.webpIllustration: Fig. 126. Local-Battery Stations with Metallic Circuithttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig127_t.webpIllustration: Fig. 127. Local-Battery Stations with Metallic Circuithttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig128_t.webpIllustration: Fig. 128. Battery in Series with Two Lineshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig129_t.webpIllustration: Fig. 129. Battery in Series with Two Lineshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig130_t.webpIllustration: Fig. 130. Bridging Battery with Repeating Coilhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig131_t.webpIllustration: Fig. 131. Bridging Battery with Impedance Coilshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig132_t.webpIllustration: Fig. 132. Double-Battery Kellogg Systemhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig133_t.webpIllustration: Fig. 133. Dean Systemhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig134_t.webpIllustration: Fig. 134. Stromberg-Carlson Systemhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig135_t.webpIllustration: Fig. 135. North Electric Company Systemhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig136_t.webpIllustration: Fig. 136. Current Supply over Parallel Limbs of Linehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig137_t.webpIllustration: Fig. 137. Current Supply over Parallel Limbs of Linehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig138_t.webpIllustration: Fig. 138. 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Principle of Broken-Line Systemhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig187_t.webpIllustration: Fig. 187. Principle of Broken-Line Systemhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig188_t.webpIllustration: Fig. 188. Poole Lock-Out Systemhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig189_t.webpIllustration: Fig. 189. K.B. Lock-Out Systemhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig190_t.webpIllustration: Fig. 190. K.B. Lock-Out Stationhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig191_t.webpIllustration: Fig. 191. K.B. Lock-Out Stationhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig192_t.webpIllustration: Fig. 192. Calling Apparatus K.B. Systemhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig193_t.webpIllustration: Fig. 193. Circuit K.B. Systemhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig194_t.webpIllustration: Fig. 194. Roberts Latching Relayhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig195_t.webpIllustration: Fig. 195. Roberts Latching Relayhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig196_t.webpIllustration: Fig. 196. Simplified Circuits of Roberts Systemhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig197_t.webpIllustration: Fig. 197. Simplified Circuits of Roberts Systemhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig198_t.webpIllustration: Fig. 198. Details of Latching Relay Connectionshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig199_t.webpIllustration: Fig. 199. Broken-Back Ringerhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig200_t.webpIllustration: Fig. 200. Details of Ringer Connectionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig201_t.webpIllustration: Fig. 201. Central-Office Impulse Transmitterhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig202_t.webpIllustration: Fig. 202. Circuits of Roberts Linehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig203_t.webpIllustration: Fig. 203. Saw Tooth Arresterhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig204_t.webpIllustration: Fig. 204. Saw-Tooth Arresterhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig205_t.webpIllustration: Fig. 205. Carbon Block Arrester?https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig206_t.webpIllustration: Fig. 206. Arrester Separatorshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig207_t.webpIllustration: Fig. 207. Carbon Block Arresterhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig208_t.webpIllustration: Fig. 208 Roberts "Self-Cleaning" Arresterhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig209_t.webpIllustration: Fig. 209. Cook Air-Gap Arresterhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig210_t.webpIllustration: Fig. 210. Western Electric Air-Gap Arresterhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig211_t.webpIllustration: Fig. 211. Kellogg Air-Gap Arresterhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig212_t.webpIllustration: Fig. 212. Vacuum Arresterhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig213_t.webpIllustration: Fig. 213. Impedance and Air-Gaphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig214_t.webpIllustration: Fig. 214. Holtzer-Cabot Arresterhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig215_t.webpIllustration: Fig. 215. Carbon Air-Gap Arresterhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig216_t.webpIllustration: Fig. 216. Mica Slip Fusehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig217_t.webpIllustration: Fig. 217. Postal Type Mica Fusehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig218_t.webpIllustration: Fig. 218. Western Union Type Mica Fusehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig219_t.webpIllustration: Fig. 219. Pair of Enclosed Fuseshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig220_t.webpIllustration: Fig. 220. Bank of Enclosed Fuseshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig221_t.webpIllustration: Fig. 221. Pair of Wooden Tube Fuseshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig222_t.webpIllustration: Fig. 222. Tubular Fuse with Asbestos Fillinghttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig223_t.webpIllustration: Fig. 223. Principle of Sneak-Current Arresterhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig224_t.webpIllustration: Fig. 224. Heat Coilhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig225_t.webpIllustration: Fig. 225. Complete Line Protectionhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig226_t.webpIllustration: Fig. 226. Sneak-Current and Air-Gap Arresterhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig227_t.webpIllustration: Fig. 227. Self-Soldering Heat-Coil Arresterhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig228_t.webpIllustration: Fig. 228. 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Clearing-Out Signalhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig246_t.webpIllustration: Fig. 246 Old-Style Drophttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig247_t.webpIllustration: Fig. 247. Tubular Drophttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig248_t.webpIllustration: Fig. 248. Strip of Tubular Dropshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig249_t.webpIllustration: Fig. 249. Drop with Night-Alarm Contactshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig250_t.webpIllustration: Fig. 250. Individual Jackhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig251_t.webpIllustration: Fig. 251. 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Dean Non-Ring-Through Cord Circuithttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig284_t.webpIllustration: Fig. 284. Monarch Non-Ring-Through Cord Circuithttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig285_t.webpIllustration: Fig. 285. Non-Ring-Through Cord Circuithttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig286_t.webpIllustration: Fig. 286. Cord Circuit with Differential Windingshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig287_t.webpIllustration: Fig. 287. Double Clearing-Out Dropshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig288_t.webpIllustration: Fig. 288. Double Clearing-Out Dropshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig289_t.webpIllustration: Fig. 289. Relay-Controlled Clearing-Out Drophttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig290_t.webpIllustration: Fig. 290. Cord Circuit with Recall Lamphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig291_t.webpIllustration: Fig. 291. Cord Circuit with Double Lamp Signalshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig292_t.webpIllustration: Fig. 292. Wall Switchboard with Telephonehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig293_t.webpIllustration: Fig. 293. 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Cord Weighthttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig299_t.webpIllustration: Fig. 299. Magneto Switchboard, Target Signals (partial)https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig300_t.webpIllustration: Fig. 300. Rear View of Target Signal, Magneto Switchboardhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig301_t.webpIllustration: Fig. 301. Dean Two-Position Switchboardhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig302_t.webpIllustration: Fig. 302. Rear View of Dean Two-Position Switchboardhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig303_t.webpIllustration: Fig. 303. Sectional Switchboard—Wall Typehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig304_t.webpIllustration: Fig. 304. Sectional Switchboard—Wall Typehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig305_t.webpIllustration: Fig. 305. Sectional Switchboard—Table Typehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyclopedia-of-telegraphy-and-telephony/images/fig306_t.webpIllustration: Fig. 306. Sectional Switchboard—Table Type 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https://openoldbooks.com/books/cymbeline/read2026-11-15T15:48:14.650Zmonthly0.6 https://openoldbooks.com/books/cymbeline-1538/read2026-11-15T15:48:14.650Zmonthly0.6 https://openoldbooks.com/books/cymbeline-1799/read2026-11-15T15:48:14.650Zmonthly0.6 https://openoldbooks.com/books/cymbeline-2269/read2026-11-15T15:48:14.650Zmonthly0.6 https://openoldbooks.com/books/cynthia/read2026-11-15T15:48:14.650Zmonthly0.6 https://openoldbooks.com/books/cynthia-ann-parker/read2026-11-15T15:48:14.650Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/cynthia-ann-parker/images/i_060.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cynthia-ann-parker/images/i_075.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cynthia-ann-parker/images/cover2.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cynthia-ann-parker/images/i_001.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cynthia-ann-parker/images/i_049.webp https://openoldbooks.com/books/cynthia-s-chauffeur/read2026-11-15T15:48:14.650Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/cynthia-s-chauffeur/images/i108.webp“You may occupy your time in any way you wish, Fitzroy,” said Cynthia.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cynthia-s-chauffeur/images/i155.webp“Now, you two—what are you discussing?”https://openoldbooks.sgp1.digitaloceanspaces.com/books/cynthia-s-chauffeur/images/i216.webp“Pity I’m not a circus lady, to balance myself on your head,” said Cynthia.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cynthia-s-chauffeur/images/i271.webpFitzroy poses as the first Earl of Chepstow.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cynthia-s-chauffeur/images/icover.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cynthia-s-chauffeur/images/i001.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cynthia-s-chauffeur/images/i003.webp“There is no lovelier garden in England than at Wells Palace.” https://openoldbooks.com/books/cynthia-s-revels/read2026-11-15T15:48:14.650Zmonthly0.6 https://openoldbooks.com/books/cynthia-steps-out/read2026-11-15T15:48:14.650Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/cynthia-steps-out/images/cover.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cynthia-steps-out/images/title.webpTitle page https://openoldbooks.com/books/cynthia-wakeham-s-money/read2026-11-15T15:48:14.650Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/cynthia-wakeham-s-money/images/acorn.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cynthia-wakeham-s-money/images/frontis.webp"‘Let me have it!’ cried Huckins. ‘I have lived in this hole for fifteen years, till I have almost rotted away like the place itself!’"https://openoldbooks.sgp1.digitaloceanspaces.com/books/cynthia-wakeham-s-money/images/swirl.webp https://openoldbooks.com/books/cyprus/read2026-11-15T15:48:14.650Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyprus/images/i020.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyprus/images/i004.webp https://openoldbooks.com/books/cyprus-as-i-saw-it-in-1879/read2026-11-15T15:48:14.650Zmonthly0.6 https://openoldbooks.com/books/cyr-readers-book-8/read2026-11-15T15:48:14.650Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyr-readers-book-8/images/enlarge-image.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyr-readers-book-8/images/illus026_sml.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyr-readers-book-8/images/illus011_sml.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyr-readers-book-8/images/illus035_sml.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyr-readers-book-8/images/illus103_sml.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyr-readers-book-8/images/illus105_sml.webpTHE ASCENT TO THE PLAINS OF ABRAHAM.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyr-readers-book-8/images/illus186_sml.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyr-readers-book-8/images/illus189_sml.webpADMIRAL NELSON.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyr-readers-book-8/images/illus198_sml.webpFrom the painting by Ernest Slingeneyer. THE DEATH OF NELSON AT TRAFALGAR.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyr-readers-book-8/images/illus243_sml.webpAfter the painting by Guizard. JOAN OF ARC.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyr-readers-book-8/images/illus045_sml.webpSTORMING THE FORTRESS.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyr-readers-book-8/images/illus047_sml.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyr-readers-book-8/images/illus049_sml.webpSIR ROGER MEETING HIS TENANTS AT CHURCH.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyr-readers-book-8/images/illus053_sml.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyr-readers-book-8/images/illus075_sml.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyr-readers-book-8/images/illus078_sml.webpMILTON DICTATING “PARADISE LOST.”https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyr-readers-book-8/images/illus116_sml.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyr-readers-book-8/images/illus126_sml.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyr-readers-book-8/images/illus128_sml.webpBIRTHPLACE OF SHAKESPEARE.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyr-readers-book-8/images/cover.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyr-readers-book-8/images/illus001_sml.webpSTRATFORD ON AVON From photograph. Copyright, 1898, Published by A. W. Elson, Boston. Engraved by Robert Varley.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyr-readers-book-8/images/illus032_sml.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyr-readers-book-8/images/illus091_sml.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyr-readers-book-8/images/illus093_sml.webpCHURCH AT STOKE POGES.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyr-readers-book-8/images/illus157_sml.webpMOUNT VERNON, THE HOME OF WASHINGTON.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyr-readers-book-8/images/music1_sml.webpMusic https://openoldbooks.com/books/cyrano-de-bergerac/read2026-11-15T15:48:14.650Zmonthly0.6 https://openoldbooks.com/books/cyrano-de-bergerac-41949/read2026-11-15T15:48:14.650Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyrano-de-bergerac-41949/images/th_illus098.webpPhotograph from Play.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyrano-de-bergerac-41949/images/th_illus112.webpPhotograph from Play.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyrano-de-bergerac-41949/images/th_illus020.webpCOQUELIN AS CYRANO DE BERGERAC.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyrano-de-bergerac-41949/images/th_illus068.webpPhotograph from Play.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyrano-de-bergerac-41949/images/th_illus166.webpPhotograph of Play.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyrano-de-bergerac-41949/images/th_illus218.webpPhotograph from Play.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyrano-de-bergerac-41949/images/th_illus238.webpPhotograph from Play.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyrano-de-bergerac-41949/images/th_illus001.webpMANSFIELD AS CYRANO DE BERGERAC.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyrano-de-bergerac-41949/images/illus002-1.webpAn Heroic Comedy in Five Actshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyrano-de-bergerac-41949/images/illus002-2.webpPublisher's Device https://openoldbooks.com/books/cyropaedia/read2026-11-15T15:48:14.650Zmonthly0.6 https://openoldbooks.com/books/cyrus-hall-mccormick/read2026-11-15T15:48:14.650Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyrus-hall-mccormick/images/fp014.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyrus-hall-mccormick/images/fp018.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyrus-hall-mccormick/images/fp022.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyrus-hall-mccormick/images/fp024.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyrus-hall-mccormick/images/fp028.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyrus-hall-mccormick/images/fp030a.webpFacsimilie part 1https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyrus-hall-mccormick/images/fp030b.webpfacsimilie part 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FIELDhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyrus-w-field-his-life-and-work/images/ill_148_sml.webpLAST TWO PAGES OF LETTER FROM MR. GLADSTONE, DATED NOVEMBER 27, 1862.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyrus-w-field-his-life-and-work/images/ill_188_sml.webpAtlantic Telegraph Cable · 1865https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyrus-w-field-his-life-and-work/images/ill_194_sml.webpTHE NIGHT-WATCHhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyrus-w-field-his-life-and-work/images/ill_264_sml.webpARDSLEY, IRVINGTON-ON-HUDSONhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyrus-w-field-his-life-and-work/images/ill_296_sml.webpCERTIFICATE OF DISCHARGEhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyrus-w-field-his-life-and-work/images/ill_302_sml.webpTHE ANDRÉ MONUMENT, TAPPAN, NEW YORKhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyrus-w-field-his-life-and-work/images/cover.webpbookcoverhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyrus-w-field-his-life-and-work/images/front_sml.webpPortrait signed of Cyrus W. Field.https://openoldbooks.sgp1.digitaloceanspaces.com/books/cyrus-w-field-his-life-and-work/images/colophon.webpcolophonhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/cyrus-w-field-his-life-and-work/images/colophon-2.webpcolophon https://openoldbooks.com/books/cytherea/read2026-11-15T15:48:14.651Zmonthly0.6 https://openoldbooks.com/books/czech-folk-tales/read2026-11-15T15:48:14.651Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/czech-folk-tales/images/p054.webpCoach with four horses and woman on side of road.https://openoldbooks.sgp1.digitaloceanspaces.com/books/czech-folk-tales/images/p070.webpWoman with dove.https://openoldbooks.sgp1.digitaloceanspaces.com/books/czech-folk-tales/images/p110.webpSt. George and the dragon, two women and text: “Hynek.”https://openoldbooks.sgp1.digitaloceanspaces.com/books/czech-folk-tales/images/p128.webpTwo men in pub; one drinking beer, another 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LONG ARS LONGA VITA BREVIS https://openoldbooks.com/books/d-p-from-tomorrow/read2026-11-15T15:48:14.651Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/d-p-from-tomorrow/images/02.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/d-p-from-tomorrow/images/cover.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/d-p-from-tomorrow/images/01.webp https://openoldbooks.com/books/d-ri-and-i-a-tale-of-daring-deeds-in-the-second-war-with-the-british-being-the-m/read2026-11-15T15:48:14.651Zmonthly0.6 https://openoldbooks.com/books/dab-kinzer-a-story-of-a-growing-boy/read2026-11-15T15:48:14.651Zmonthly0.6 https://openoldbooks.com/books/dactylography-or-the-study-of-fingerprints/read2026-11-15T15:48:14.651Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/dactylography-or-the-study-of-fingerprints/images/010.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/dactylography-or-the-study-of-fingerprints/images/019.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/dactylography-or-the-study-of-fingerprints/images/020.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/dactylography-or-the-study-of-fingerprints/images/029.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/dactylography-or-the-study-of-fingerprints/images/032.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/dactylography-or-the-study-of-fingerprints/images/039fp.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/dactylography-or-the-study-of-fingerprints/images/043a.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/dactylography-or-the-study-of-fingerprints/images/043b.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/dactylography-or-the-study-of-fingerprints/images/047a.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/dactylography-or-the-study-of-fingerprints/images/047b.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/dactylography-or-the-study-of-fingerprints/images/068.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/dactylography-or-the-study-of-fingerprints/images/069.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/dactylography-or-the-study-of-fingerprints/images/069a.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/dactylography-or-the-study-of-fingerprints/images/069b.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/dactylography-or-the-study-of-fingerprints/images/071.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/dactylography-or-the-study-of-fingerprints/images/072.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/dactylography-or-the-study-of-fingerprints/images/073.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/dactylography-or-the-study-of-fingerprints/images/c.webpfragmented letter Chttps://openoldbooks.sgp1.digitaloceanspaces.com/books/dactylography-or-the-study-of-fingerprints/images/e.webpfragmented letter Ehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/dactylography-or-the-study-of-fingerprints/images/invj.webpinverted letter Jhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/dactylography-or-the-study-of-fingerprints/images/100.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/dactylography-or-the-study-of-fingerprints/images/invu.webpinverted Uhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/dactylography-or-the-study-of-fingerprints/images/cover.webpBook coverhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/dactylography-or-the-study-of-fingerprints/images/frontisa.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/dactylography-or-the-study-of-fingerprints/images/frontisb.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/dactylography-or-the-study-of-fingerprints/images/frontisc.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/dactylography-or-the-study-of-fingerprints/images/logo.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/dactylography-or-the-study-of-fingerprints/images/052.webp https://openoldbooks.com/books/dad/read2026-11-15T15:48:14.651Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/dad/images/cover.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/dad/images/frontispiece.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/dad/images/colophon.webp https://openoldbooks.com/books/daddy-do-funny-s-wisdom-jingles/read2026-11-15T15:48:14.651Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-do-funny-s-wisdom-jingles/images/img21.500.webpTHE WATERMELONhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-do-funny-s-wisdom-jingles/images/img22.500.webpTHE GOURDhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-do-funny-s-wisdom-jingles/images/img024.webpTHE MOSQUITOhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-do-funny-s-wisdom-jingles/images/img025.webpCONFESSIONhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-do-funny-s-wisdom-jingles/images/img029.webpTHE GRUBWORMhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-do-funny-s-wisdom-jingles/images/img030.webpRAIN OR SHINEhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-do-funny-s-wisdom-jingles/images/img033.webpTHE FLYhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-do-funny-s-wisdom-jingles/images/img037.webpTHE AMBITIOUS COWhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-do-funny-s-wisdom-jingles/images/img039.webpJACK-O'LANTERNhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-do-funny-s-wisdom-jingles/images/img041.webpWILL O' THE WISPhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-do-funny-s-wisdom-jingles/images/img044.webpTHE MONKEYhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-do-funny-s-wisdom-jingles/images/img045.webpTHE ARISTOCRAThttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-do-funny-s-wisdom-jingles/images/img046.webpTHE CRAWFISHhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-do-funny-s-wisdom-jingles/images/img048.webpTHE CHIMNEY-SWALLOWhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-do-funny-s-wisdom-jingles/images/img50.webpTHE PORCUPINEhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-do-funny-s-wisdom-jingles/images/img54.webpTHE PERSIMMONhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-do-funny-s-wisdom-jingles/images/img55.webpIN HARNESShttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-do-funny-s-wisdom-jingles/images/img56.webpTHE CANARYhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-do-funny-s-wisdom-jingles/images/img57.webpANSWERING BACKhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-do-funny-s-wisdom-jingles/images/img61.webpTHE NEW RICHhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-do-funny-s-wisdom-jingles/images/img64.webpTHE TURKEY-GOBBLERhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-do-funny-s-wisdom-jingles/images/img65.webpTHE CAULIFLOWERhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-do-funny-s-wisdom-jingles/images/img66.webpTHE STEPMOTHERhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-do-funny-s-wisdom-jingles/images/img67.webpTHE FROGhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-do-funny-s-wisdom-jingles/images/img68.webpTHE RAThttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-do-funny-s-wisdom-jingles/images/img71.webpTHE MEASURING WORMhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-do-funny-s-wisdom-jingles/images/img72.webpTHE TOP-KNOT HENhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-do-funny-s-wisdom-jingles/images/img73.webpTOO FAMILIARhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-do-funny-s-wisdom-jingles/images/img74.webpTHE 'POSSUMhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-do-funny-s-wisdom-jingles/images/img84.webpTHE MIRRORhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-do-funny-s-wisdom-jingles/images/img77.webpTHE CATERPILLARhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-do-funny-s-wisdom-jingles/images/img78.webpDR. DRAKEhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-do-funny-s-wisdom-jingles/images/img79.webpTHE PEACOCKhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-do-funny-s-wisdom-jingles/images/img80.webpTHE ALLIGATORhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-do-funny-s-wisdom-jingles/images/img81.webpTHE TERRAPINhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-do-funny-s-wisdom-jingles/images/img82.webpTHE DANDELIONhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-do-funny-s-wisdom-jingles/images/img83.webpTHE CUDhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-do-funny-s-wisdom-jingles/images/img86.webpTHE PEThttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-do-funny-s-wisdom-jingles/images/img87.webpTHE GUINEA-HENhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-do-funny-s-wisdom-jingles/images/img88.webpTHE MOONhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-do-funny-s-wisdom-jingles/images/img90.webpA GUILTY CONSCIENCEhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-do-funny-s-wisdom-jingles/images/img91.webpTHE BAThttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-do-funny-s-wisdom-jingles/images/img93.webpTHE FIREFLYhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-do-funny-s-wisdom-jingles/images/img94.webpTHE THISTLEhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-do-funny-s-wisdom-jingles/images/img95.webpTHE GRAY SQUIRRELhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-do-funny-s-wisdom-jingles/images/img98.webpTHE LOCOMOTIVEhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-do-funny-s-wisdom-jingles/images/img99.webpTHE GOAThttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-do-funny-s-wisdom-jingles/images/img103.webpTHE ENDLESS SONGhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-do-funny-s-wisdom-jingles/images/img105.webpTHE RAIN-CROWhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-do-funny-s-wisdom-jingles/images/img107.webpTHE BLACK SHEEPhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-do-funny-s-wisdom-jingles/images/img038.webpTRIED BY FIREhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-do-funny-s-wisdom-jingles/images/img043.webpTHE RUNThttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-do-funny-s-wisdom-jingles/images/img011.webpCONTENTShttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-do-funny-s-wisdom-jingles/images/img026.webpTHE GAME-COCKhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-do-funny-s-wisdom-jingles/images/img20.400.webpTHE WRENhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-do-funny-s-wisdom-jingles/images/img027.webpTHE EPICUREhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-do-funny-s-wisdom-jingles/images/img34.webpTHE LITTLE CHICKENhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-do-funny-s-wisdom-jingles/images/img035.webpTHE SCARE-CROWhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-do-funny-s-wisdom-jingles/images/img036.webpTHE SCARE-CROWhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-do-funny-s-wisdom-jingles/images/img047.webpTHE ANGLEWORMhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-do-funny-s-wisdom-jingles/images/img49.webpCATCHING DOODLE-BUGShttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-do-funny-s-wisdom-jingles/images/img53.webpTHE RATTLE-SNAKEhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-do-funny-s-wisdom-jingles/images/img59.webpDAT'S DE WAY MY LADY'LL DOhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-do-funny-s-wisdom-jingles/images/img60.webpTHE MAMMY ALLIGATORhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-do-funny-s-wisdom-jingles/images/img62.webpTHE WIBBLY WABBLY CALFhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-do-funny-s-wisdom-jingles/images/img63.webpTHE WIBBLY WABBLY CALFhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-do-funny-s-wisdom-jingles/images/img70.webpTHE MUSHROOMhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-do-funny-s-wisdom-jingles/images/img76.webpTHE CHAMELEONhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-do-funny-s-wisdom-jingles/images/img85.webpGOSLINGShttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-do-funny-s-wisdom-jingles/images/img92.webpINCUBATOR CHICKENShttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-do-funny-s-wisdom-jingles/images/img96.webpLOOK OUT FOR MISTER BEEhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-do-funny-s-wisdom-jingles/images/img101.webpTHE FRIZZLED CHICKENhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-do-funny-s-wisdom-jingles/images/img108.webpTHE PRIZE-WINNERhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-do-funny-s-wisdom-jingles/images/img109.webpTHE DOG https://openoldbooks.com/books/daddy-jake-the-runaway/read2026-11-15T15:48:14.651Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-jake-the-runaway/images/p087.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-jake-the-runaway/images/p105.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-jake-the-runaway/images/p115.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-jake-the-runaway/images/p127.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-jake-the-runaway/images/p159.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-jake-the-runaway/images/p175.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-jake-the-runaway/images/frontis.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-jake-the-runaway/images/titlepagea.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-jake-the-runaway/images/titlepageb.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-jake-the-runaway/images/titlepagec.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-jake-the-runaway/images/p009.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-jake-the-runaway/images/p019.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-jake-the-runaway/images/p025.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-jake-the-runaway/images/p029.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-jake-the-runaway/images/p034.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-jake-the-runaway/images/p041.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-jake-the-runaway/images/p049.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-jake-the-runaway/images/p057.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-jake-the-runaway/images/p063.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-jake-the-runaway/images/p071.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-jake-the-runaway/images/p075.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-jake-the-runaway/images/p079.webp https://openoldbooks.com/books/daddy-joe-s-fiddle/read2026-11-15T15:48:14.651Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-joe-s-fiddle/images/i001_inside_front_cover.webpinside front coverhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-joe-s-fiddle/images/i_title.webptitle pagehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-joe-s-fiddle/images/i_titlelogo.webplogohttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-joe-s-fiddle/images/i051.webpSHALL I ASK OUR FATHER?https://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-joe-s-fiddle/images/i071.webpSHE STOOD A MOMENT IN MEDITATIONhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-joe-s-fiddle/images/i091.webpI’VE SAVED YOU FROM THE GREAT WI-WILL-MECQhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-joe-s-fiddle/images/i097.webpIT WAS AS THOUGH ALL THE PLAINTIVE STORY OF A DYING RACE HAD BEEN STORED IN THAT LITTLE RED CASEhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-joe-s-fiddle/images/coversmall.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-joe-s-fiddle/images/i003_frontis.webpCHEE’S FACE GLOWED. SHE WOULD MAKE MUSIC FOR HERSELFhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-joe-s-fiddle/images/i032.webpTHIS IS A ’PORTANT MATTER https://openoldbooks.com/books/daddy-long-legs/read2026-11-15T15:48:14.651Zmonthly0.6 https://openoldbooks.com/books/daddy-long-legs-40426/read2026-11-15T15:48:14.651Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-long-legs-40426/images/pic_titlepage.webplong-legged man with short-legged doghttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-long-legs-40426/images/plateII.webpJudy with a laughing group of orphans, showing one of her drawingshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-long-legs-40426/images/pic35.webpANY ORPHAN / Rear Elevation / Front Elevationhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-long-legs-40426/images/pic40.webpJudy at Basket Ballhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-long-legs-40426/images/pic45.webptall thin manhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-long-legs-40426/images/pic57.webpprocession of girlshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-long-legs-40426/images/pic63.webpNEWS of the MONTH / Judy learns to skate / And to vault a bar (Legs are very difficult.) / Also to slide down a rope / She receives two flunk notes and sheds many tears / But promises to study HARDhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-long-legs-40426/images/pic69.webpJudy with her head in a bandagehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-long-legs-40426/images/pic75.webpcentipedehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-long-legs-40426/images/pic85.webpa fat Trusteehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-long-legs-40426/images/pic92.webpthe farm househttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-long-legs-40426/images/pic93.webphilly landscapehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-long-legs-40426/images/pic99.webplong-legged calfhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-long-legs-40426/images/pic100.webpButtercup Daisy Birdie Bess Spotty (I can’t draw cows!)https://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-long-legs-40426/images/pic101.webpdaddy-long-legs spiderhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-long-legs-40426/images/pic107.webpJudy thin and fathttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-long-legs-40426/images/pic109.webpfloor planhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-long-legs-40426/images/pic114.webpMcBRIDE FOREVERhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-long-legs-40426/images/pic124a.webppouring rain on umbrellashttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-long-legs-40426/images/pic124b.webppouring rain on umbrellashttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-long-legs-40426/images/pic129.webpIt’s the early bird that catches the tub.https://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-long-legs-40426/images/pic150.webpJudy Wins the Fifty Yard Dashhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-long-legs-40426/images/pic155.webp“My dear Mrs. Centipede, will you have one lump or two?”https://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-long-legs-40426/images/pic172.webpnine young pigshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-long-legs-40426/images/pic173.webphen with three chickshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-long-legs-40426/images/pic175.webpJudy in her new hathttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-long-legs-40426/images/pic177.webpOld Grove is perfectly safe.https://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-long-legs-40426/images/pic184.webphorsehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-long-legs-40426/images/pic189.webpturtlehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-long-legs-40426/images/pic190.webpskull and crossboneshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-long-legs-40426/images/plateIII.webpJudy with Julia, Sallie, Jervis and other friendshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-long-legs-40426/images/pic205.webpThis is the only picture extant of a stereognathus. He has a head like a snake and ears like a dog and feet like a cow and a tail like a lizard and wings like a swan and is covered with nice soft fur like a sweet little pussy cat.https://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-long-legs-40426/images/pic226.webpgirls greeting the rising sunhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-long-legs-40426/images/pic227.webpThis is Prexy’s kitten. You can see from the picture how Angora he is.https://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-long-legs-40426/images/pic230.webpJudy learning to swimhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-long-legs-40426/images/pic256.webpline of dancing girlshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-long-legs-40426/images/pic257.webpfurniture van addressed to Daddy Long Legshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-long-legs-40426/images/plateIV.webpJudy embraces Jerviehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-long-legs-40426/images/ads_2.webppicture of bookhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-long-legs-40426/images/ads_3.webppicture of bookhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-long-legs-40426/images/ads_6.webppicture of bookhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-long-legs-40426/images/old_cover.webpimage of book spinehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-long-legs-40426/images/spine.webpimage of book spinehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-long-legs-40426/images/cover.webpimage of front coverhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-long-legs-40426/images/plateI.webpJudy in gingham, carrying a tea tray https://openoldbooks.com/books/daddy-long-legs-75857/read2026-11-15T15:48:14.651Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-long-legs-75857/images/08-plate.webpThe girls sit at the table, their backs turned, as Freddie pours salt into the sugar bowl.https://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-long-legs-75857/images/26-plate.webpThe children are gathered around the drawing of the Trusteehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-long-legs-75857/images/32-plate.webpJudy points accusingly at the trustees.https://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-long-legs-75857/images/54-plate.webpJudy leans against the closed door of the room as the others look at her from across the stage.https://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-long-legs-75857/images/111-plate.webpWalters stands in front of Judy, who leans nervously against the armchairhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-long-legs-75857/images/141-stage.webpStage diagram of Act I: The Orphan Asylumhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-long-legs-75857/images/142-stage.webpStage diagram of Act II: Judy’s Study at Collegehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-long-legs-75857/images/143-stage.webpStage diagram of Act III: Sitting Room at Farm Househttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-long-legs-75857/images/144-stage.webpSimplified stage diagram of Act III: Sitting Room of Farm Househttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-long-legs-75857/images/145-stage.webpStage diagram of Act IV: Pendleton’s Libraryhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-long-legs-75857/images/title-page.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-long-legs-75857/images/bracket.webpBracket connecting the last six names in the list. https://openoldbooks.com/books/daddy-s-bedtime-bird-stories/read2026-11-15T15:48:14.651Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-s-bedtime-bird-stories/images/img006.webpA Gray Bird Was Flying Overhead.https://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-s-bedtime-bird-stories/images/img007.webpI'm ready now, said Dr. Raven.https://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-s-bedtime-bird-stories/images/img009.webpThe Robins Agreed It was a Good Scheme.https://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-s-bedtime-bird-stories/images/img010.webpMongo Got Quite a Bit Ahead.https://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-s-bedtime-bird-stories/images/img012.webpOne Little Chickadee Sang a Solo.https://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-s-bedtime-bird-stories/images/img014.webpIn a Few Minutes Mr. Robin Came.https://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-s-bedtime-bird-stories/images/img015.webpHe Walked on Her Hand.https://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-s-bedtime-bird-stories/images/img016.webpIN THE AFTERNOONS ELIZABETH LETS HIM OUT OF HIS CAGE.https://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-s-bedtime-bird-stories/images/img017.webpThe Bird Sat on His Hand.https://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-s-bedtime-bird-stories/images/img019.webpThey Fired Them Off Quickly.https://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-s-bedtime-bird-stories/images/img020.webpNice old lady will hear our voices.https://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-s-bedtime-bird-stories/images/img021.webpWould you like to join us?https://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-s-bedtime-bird-stories/images/img022.webpIt's a man.https://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-s-bedtime-bird-stories/images/img023.webpOne Bird Seemed to be the Leader.https://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-s-bedtime-bird-stories/images/img024.webpSmacked Their Little Beaks.https://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-s-bedtime-bird-stories/images/img026.webpHe Put the Book Before Him.https://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-s-bedtime-bird-stories/images/img027.webpWE'VE BEEN ON THIS CHAIR SO LONG, SAID THE FOURTH EAGLE.https://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-s-bedtime-bird-stories/images/img028.webpWho Should Arrive but Fairies.https://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-s-bedtime-bird-stories/images/img030.webpThey Promised to Wait on Guests.https://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-s-bedtime-bird-stories/images/img031.webpThe Bird Began to Recover.https://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-s-bedtime-bird-stories/images/img032.webpMr. Hippopotamus Was Having His Bath.https://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-s-bedtime-bird-stories/images/img035.webpWaited on All Who Came.https://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-s-bedtime-bird-stories/images/img036.webpShrieked at the Top of Her Lungs.https://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-s-bedtime-bird-stories/images/img038.webpHe Hid His Face in Shame.https://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-s-bedtime-bird-stories/images/img039.webpHow the Bats do Love the Night!https://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-s-bedtime-bird-stories/images/img040.webpJim Ducked Him in the Brook.https://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-s-bedtime-bird-stories/images/img041.webpShe Watched the Little Bird.https://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-s-bedtime-bird-stories/images/img042.webpWe'll have our hose ready.https://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-s-bedtime-bird-stories/images/img004.webpOld Mr. Owl Danced with the Rest.https://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-s-bedtime-bird-stories/images/img001.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-s-bedtime-bird-stories/images/img002.webpMR. OWL AWAKENED THE FAIRIES AND TOLD THEM TO LISTEN TO HIS BOOK.https://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-s-bedtime-bird-stories/images/img003.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-s-bedtime-bird-stories/images/img005.webpMr. and Mrs. Seagull Flew Off with Bluey.https://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-s-bedtime-bird-stories/images/img008.webpHe Sang His Song Several Times.https://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-s-bedtime-bird-stories/images/img011.webpOne Little Bird Found a Crumb.https://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-s-bedtime-bird-stories/images/img013.webpThey Took Little Flying Trips.https://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-s-bedtime-bird-stories/images/img018.webpThe Eagle Was Flying Overhead.https://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-s-bedtime-bird-stories/images/img025.webpHe is Very Brave.https://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-s-bedtime-bird-stories/images/img029.webpThe Grand Opera Chorus.https://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-s-bedtime-bird-stories/images/img033.webpSaving the Little Birds from Danger.https://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-s-bedtime-bird-stories/images/img034.webpTHE MOTHER HUMMING-BIRD HURRIED BACK.https://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-s-bedtime-bird-stories/images/img037.webpAll the Little Boys Helped. https://openoldbooks.com/books/daddy-s-girl/read2026-11-15T15:48:14.651Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-s-girl/images/illus2.webp“A perfect person could not tell a lie, could she?” asked Sibyl.—Page 123. Daddy’s Girl.https://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-s-girl/images/illus3.webp“Shall I find mother for you?” asked Sibyl, leading Lord Grayleigh across the lawn.—Page 208. Daddy’s Girl.https://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-s-girl/images/illus4.webpAn old woman wearing a bedgown, and with a cap with a large frill, appeared in the porch of the tiny cottage.—Page 224. Daddy’s Girl.https://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-s-girl/images/cover.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-s-girl/images/illus1.webpDADDY’S GIRL. Frontispiece. https://openoldbooks.com/books/daddy-s-little-rhyme-book/read2026-11-15T15:48:14.651Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-s-little-rhyme-book/images/p04.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-s-little-rhyme-book/images/p05.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-s-little-rhyme-book/images/p08.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-s-little-rhyme-book/images/p09.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-s-little-rhyme-book/images/p10.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-s-little-rhyme-book/images/p12.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-s-little-rhyme-book/images/p13.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-s-little-rhyme-book/images/cover.webpDaddy’s Little Rhyme Bookhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-s-little-rhyme-book/images/p06.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-s-little-rhyme-book/images/p07.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-s-little-rhyme-book/images/p11.webp https://openoldbooks.com/books/daddy-takes-us-skating/read2026-11-15T15:48:14.651Zmonthly0.6 https://openoldbooks.com/books/daddy-takes-us-to-the-garden/read2026-11-15T15:48:14.651Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-takes-us-to-the-garden/images/3-tb.webpTomato Standhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-takes-us-to-the-garden/images/34-tb.webpLooking Out the Windowhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-takes-us-to-the-garden/images/94-tb.webpIn the Rainhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-takes-us-to-the-garden/images/132-tb.webpWorking in the Gardenhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-takes-us-to-the-garden/images/coverpicture.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daddy-takes-us-to-the-garden/images/emblem.webpEmblem https://openoldbooks.com/books/daedalus/read2026-11-15T15:48:14.651Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/daedalus/images/i_title-logo.webplogo https://openoldbooks.com/books/daemonologie/read2026-11-15T15:48:14.651Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/daemonologie/images/083.webpIllustration: Country Scenehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daemonologie/images/088.webpIllustration: Examination of several witcheshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daemonologie/images/103.webpIllustration: Country scene with cattle and churchhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daemonologie/images/108.webpIllustration: Street scene: Two men and a woman https://openoldbooks.com/books/daffydowndilly-and-the-golden-touch/read2026-11-15T15:48:14.651Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/daffydowndilly-and-the-golden-touch/images/i007.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daffydowndilly-and-the-golden-touch/images/i021.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daffydowndilly-and-the-golden-touch/images/cover.webp https://openoldbooks.com/books/dagonet-abroad/read2026-11-15T15:48:14.651Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/dagonet-abroad/images/cover.webp[Image of the book's cover unavailable.]https://openoldbooks.sgp1.digitaloceanspaces.com/books/dagonet-abroad/images/colophon.webp https://openoldbooks.com/books/dagonet-ditties/read2026-11-15T15:48:14.651Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/dagonet-ditties/images/i_dropcap_t.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/dagonet-ditties/images/i_dropcap_s.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/dagonet-ditties/images/i_dropcap_i.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/dagonet-ditties/images/i_dropcap_a.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/dagonet-ditties/images/i_dropcap_o.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/dagonet-ditties/images/i_dropcap_m.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/dagonet-ditties/images/i_dropcap_u.webp“Uhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/dagonet-ditties/images/i_dropcap_b.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/dagonet-ditties/images/i_dropcap_c.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/dagonet-ditties/images/i_dropcap_y.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/dagonet-ditties/images/i_dropcap_w.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/dagonet-ditties/images/i_dropcap_h.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/dagonet-ditties/images/i_dropcap_l.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/dagonet-ditties/images/i_dropcap_f.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/dagonet-ditties/images/i_dropcap_r.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/dagonet-ditties/images/i_dropcap_g.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/dagonet-ditties/images/cover.webp[Image of the book]https://openoldbooks.sgp1.digitaloceanspaces.com/books/dagonet-ditties/images/colophon.webp https://openoldbooks.com/books/dahcotah-life-and-legends-of-the-sioux-around-fort-snelling/read2026-11-15T15:48:14.651Zmonthly0.6 https://openoldbooks.com/books/daily-lesson-plans-in-english/read2026-11-15T15:48:14.651Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/daily-lesson-plans-in-english/images/cover.webpbook cover https://openoldbooks.com/books/daily-stories-of-pennsylvania/read2026-11-15T15:48:14.651Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/daily-stories-of-pennsylvania/images/drop_t.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daily-stories-of-pennsylvania/images/drop_a.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daily-stories-of-pennsylvania/images/drop_f.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daily-stories-of-pennsylvania/images/drop_i.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daily-stories-of-pennsylvania/images/drop_j.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daily-stories-of-pennsylvania/images/drop_n.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daily-stories-of-pennsylvania/images/drop_p.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daily-stories-of-pennsylvania/images/drop_g.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daily-stories-of-pennsylvania/images/drop_m.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daily-stories-of-pennsylvania/images/drop_b.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daily-stories-of-pennsylvania/images/drop_w.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daily-stories-of-pennsylvania/images/drop_r.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daily-stories-of-pennsylvania/images/drop_s.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daily-stories-of-pennsylvania/images/drop_d.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daily-stories-of-pennsylvania/images/drop_v.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daily-stories-of-pennsylvania/images/drop_o.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daily-stories-of-pennsylvania/images/drop_c.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daily-stories-of-pennsylvania/images/drop_y.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daily-stories-of-pennsylvania/images/drop_e.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daily-stories-of-pennsylvania/images/drop_l.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daily-stories-of-pennsylvania/images/drop_q.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daily-stories-of-pennsylvania/images/cover.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daily-stories-of-pennsylvania/images/frontis.webpPA State Capitol Buildinghttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daily-stories-of-pennsylvania/images/titlepage.webplogohttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daily-stories-of-pennsylvania/images/verso.webppublisher logohttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daily-stories-of-pennsylvania/images/dedication.webpsignature https://openoldbooks.com/books/daily-strength-for-daily-needs/read2026-11-15T15:48:14.651Zmonthly0.6 https://openoldbooks.com/books/daily-thoughts/read2026-11-15T15:48:14.651Zmonthly0.6 https://openoldbooks.com/books/daily-training/read2026-11-15T15:48:14.651Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/daily-training/images/img-80a_sml.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daily-training/images/img-80b_sml.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daily-training/images/img-80c_sml.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daily-training/images/img-81_sml.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daily-training/images/img-82a_sml.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daily-training/images/img-82b_sml.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daily-training/images/img-83a_sml.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daily-training/images/img-83b_sml.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daily-training/images/img-84_sml.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daily-training/images/cover.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daily-training/images/deco.webptext decorationhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daily-training/images/colohon.webpcolophon, K https://openoldbooks.com/books/dainty-s-cruel-rivals/read2026-11-15T15:48:14.651Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/dainty-s-cruel-rivals/images/cover.webpbook cover https://openoldbooks.com/books/daireen/read2026-11-15T15:48:14.651Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/daireen/images/frontispiece.webpfrontispiecehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daireen/images/enlarge.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daireen/images/titlepage1.webptitlepage1https://openoldbooks.sgp1.digitaloceanspaces.com/books/daireen/images/titlepage2.webptitlepage2https://openoldbooks.sgp1.digitaloceanspaces.com/books/daireen/images/titlepage3.webptitlepage3 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https://openoldbooks.com/books/daisy-27949/read2026-11-15T15:48:14.651Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/daisy-27949/images/i002.webp"'And you love Jesus, Darry,' I said."https://openoldbooks.sgp1.digitaloceanspaces.com/books/daisy-27949/images/logo.webplogohttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daisy-27949/images/banner.webpBar Line https://openoldbooks.com/books/daisy-ashford-her-book/read2026-11-15T15:48:14.651Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/daisy-ashford-her-book/images/cover.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daisy-ashford-her-book/images/flyleaves.webpInside Coverhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daisy-ashford-her-book/images/emblem.webpEmblem https://openoldbooks.com/books/daisy-brooks/read2026-11-15T15:48:14.651Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/daisy-brooks/images/illus-ad1.webpad pagehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daisy-brooks/images/illus-ad2.webpad pagehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daisy-brooks/images/illus-ad3.webpad pagehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daisy-brooks/images/illus-ad4.webpad pagehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daisy-brooks/images/illus-ad5.webpad pagehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daisy-brooks/images/illus-ad6.webpad pagehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daisy-brooks/images/illus-ad7.webpad pagehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daisy-brooks/images/illus-ad8.webpad pagehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daisy-brooks/images/daisy-cvr.webp https://openoldbooks.com/books/daisy-burns-volume-1/read2026-11-15T15:48:14.651Zmonthly0.6 https://openoldbooks.com/books/daisy-burns-volume-2/read2026-11-15T15:48:14.651Zmonthly0.6 https://openoldbooks.com/books/daisy-by-margaret-marshall-saunders/read2026-11-15T15:48:14.651Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/daisy-by-margaret-marshall-saunders/images/02-illo.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daisy-by-margaret-marshall-saunders/images/10-illo.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daisy-by-margaret-marshall-saunders/images/29-illo.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daisy-by-margaret-marshall-saunders/images/53-illo.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daisy-by-margaret-marshall-saunders/images/59-illo.webp https://openoldbooks.com/books/daisy-dare/read2026-11-15T15:48:14.651Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/daisy-dare/images/ill-057b-s.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daisy-dare/images/ill-063.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daisy-dare/images/ill-007b-t.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daisy-dare/images/ill-012.webp"Oh, do not mock me, Daisy Dare, With your small hands so soft and fair."https://openoldbooks.sgp1.digitaloceanspaces.com/books/daisy-dare/images/ill-024.webp"She wandered hopeless to the strand, And, hopeless, westward waved her hand."https://openoldbooks.sgp1.digitaloceanspaces.com/books/daisy-dare/images/ill-028.webpShip going downhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daisy-dare/images/ill-030.webp"Turning her white cheek from the light, Clasping her small hands fiercely tight!"https://openoldbooks.sgp1.digitaloceanspaces.com/books/daisy-dare/images/ill-031a.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daisy-dare/images/ill-031b-w.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daisy-dare/images/ill-043.webp"Two figures smote her 'wildered sight, And left two blots upon the light."https://openoldbooks.sgp1.digitaloceanspaces.com/books/daisy-dare/images/ill-053.webpCavernhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daisy-dare/images/ill-054.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daisy-dare/images/ill-055a.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daisy-dare/images/ill-001a.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daisy-dare/images/ill-001b.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daisy-dare/images/ill-002.webpHandwritten: Truly Yrs, Rosa V Jeffreyhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daisy-dare/images/ill-003.webpEmblemhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daisy-dare/images/ill-005a.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daisy-dare/images/ill-005b.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daisy-dare/images/ill-006.webp"At early morn swept Daisy Dare,— Sparkling, graceful, passing fair.">https://openoldbooks.sgp1.digitaloceanspaces.com/books/daisy-dare/images/ill-007a.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daisy-dare/images/ill-055b.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daisy-dare/images/ill-056.webpMULLEN, PHOTO "Six little feet to cover, Six little hands to fill, Tumbling out in the clover, Stumbling over the sill."https://openoldbooks.sgp1.digitaloceanspaces.com/books/daisy-dare/images/ill-057a.webp https://openoldbooks.com/books/daisy-herself/read2026-11-15T15:48:14.651Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/daisy-herself/images/cover.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daisy-herself/images/logo.webplogo https://openoldbooks.com/books/daisy-in-the-field/read2026-11-15T15:48:14.651Zmonthly0.6 https://openoldbooks.com/books/daisy-miller-a-study/read2026-11-15T15:48:14.651Zmonthly0.6 https://openoldbooks.com/books/daisy-of-old-meadow/read2026-11-15T15:48:14.651Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/daisy-of-old-meadow/images/image001.webpimage001https://openoldbooks.sgp1.digitaloceanspaces.com/books/daisy-of-old-meadow/images/image002.webpimage002https://openoldbooks.sgp1.digitaloceanspaces.com/books/daisy-of-old-meadow/images/image003.webpimage003https://openoldbooks.sgp1.digitaloceanspaces.com/books/daisy-of-old-meadow/images/image004.webpimage004https://openoldbooks.sgp1.digitaloceanspaces.com/books/daisy-of-old-meadow/images/image005.webpimage005 https://openoldbooks.com/books/daisy-or-the-fairy-spectacles/read2026-11-15T15:48:14.651Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/daisy-or-the-fairy-spectacles/images/image01_frontispiece.webpDAISY THOUGHT MORE OF BUTTERFLIES THAN OF BIRDS.https://openoldbooks.sgp1.digitaloceanspaces.com/books/daisy-or-the-fairy-spectacles/images/image02_chap01.webpSHE PUT THE GIRL'S HAND INTO HIS.https://openoldbooks.sgp1.digitaloceanspaces.com/books/daisy-or-the-fairy-spectacles/images/image03_chap09.webpTHE LOAF AND FLASKhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daisy-or-the-fairy-spectacles/images/image04_chap21.webpAND HE LOOKED INTO MY FACE. https://openoldbooks.com/books/daisy-s-aunt/read2026-11-15T15:48:14.651Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/daisy-s-aunt/images/logo1.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daisy-s-aunt/images/flourish2a.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daisy-s-aunt/images/auntdaisy.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daisy-s-aunt/images/flourish1b.webp https://openoldbooks.com/books/daisy-s-necklace-and-what-came-of-it/read2026-11-15T15:48:14.651Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/daisy-s-necklace-and-what-came-of-it/images/p125.webpCrosshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daisy-s-necklace-and-what-came-of-it/images/p202.webpCrosshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daisy-s-necklace-and-what-came-of-it/images/p020.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daisy-s-necklace-and-what-came-of-it/images/p176.webpJ. G. Burbank, Attorney at Law. https://openoldbooks.com/books/daisy-s-work/read2026-11-15T15:48:14.651Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/daisy-s-work/images/i-011b.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daisy-s-work/images/i-013.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/daisy-s-work/images/i-023.webpboy and girl and 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pagehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/dame-wonder-s-picture-alphabet/images/illus-0004-t.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/dame-wonder-s-picture-alphabet/images/illus-0005.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/dame-wonder-s-picture-alphabet/images/illus-0006.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/dame-wonder-s-picture-alphabet/images/illus-0007.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/dame-wonder-s-picture-alphabet/images/illus-0008.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/dame-wonder-s-picture-alphabet/images/illus-0009.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/dame-wonder-s-picture-alphabet/images/illus-0010.webp https://openoldbooks.com/books/dames/read2026-11-15T15:48:14.651Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/dames/images/image1.webpTwo men on a beach at night https://openoldbooks.com/books/damn-a-book-of-calumny/read2026-11-15T15:48:14.651Zmonthly0.6 https://openoldbooks.com/books/damned/read2026-11-15T15:48:14.651Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/damned/images/cover.webp https://openoldbooks.com/books/damned-if-you-don-t/read2026-11-15T15:48:14.651Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/damned-if-you-don-t/images/i002.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/damned-if-you-don-t/images/i003.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/damned-if-you-don-t/images/i004.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/damned-if-you-don-t/images/i005.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/damned-if-you-don-t/images/i006.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/damned-if-you-don-t/images/i007.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/damned-if-you-don-t/images/cover.webp https://openoldbooks.com/books/damon-and-delia/read2026-11-15T15:48:14.651Zmonthly0.6 https://openoldbooks.com/books/dan-carter-and-the-cub-honor/read2026-11-15T15:48:14.651Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/dan-carter-and-the-cub-honor/images/cover.webpDan Carter and the Cub Honorhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/dan-carter-and-the-cub-honor/images/front.webpThe Cubs spent every spare hour in the church gymnasium. https://openoldbooks.com/books/dan-carter-and-the-great-carved-face/read2026-11-15T15:48:14.651Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/dan-carter-and-the-great-carved-face/images/cover.webpDan Carter and the Great Carved Facehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/dan-carter-and-the-great-carved-face/images/front.webpA grotesque carved face loomed on the wall. https://openoldbooks.com/books/dan-carter-and-the-haunted-castle/read2026-11-15T15:48:14.651Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/dan-carter-and-the-haunted-castle/images/cover.webpDan Carter and the Haunted Castlehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/dan-carter-and-the-haunted-castle/images/front.webp“Dan, you made a bull’s-eye!” https://openoldbooks.com/books/dan-carter-and-the-money-box/read2026-11-15T15:48:14.651Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/dan-carter-and-the-money-box/images/cover.webpDan Carter and the Money Boxhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/dan-carter-and-the-money-box/images/front.webpTriumphantly, he brought out the tin box. https://openoldbooks.com/books/dan-carter-cub-scout/read2026-11-15T15:48:14.651Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/dan-carter-cub-scout/images/cover.webpDan Carter—Cub Scouthttps://openoldbooks.sgp1.digitaloceanspaces.com/books/dan-carter-cub-scout/images/front.webpHe opened the creaking door and peered inside. https://openoldbooks.com/books/dan-carter-cub-scout-and-the-river-camp/read2026-11-15T15:48:14.651Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/dan-carter-cub-scout-and-the-river-camp/images/cover.webpDan Carter—Cub Scout and the River Camphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/dan-carter-cub-scout-and-the-river-camp/images/front.webpHe had found a small cardboard box. https://openoldbooks.com/books/dan-merrithew/read2026-11-15T15:48:14.651Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/dan-merrithew/images/img-090.webp"Oh, father," broke in the girl, "tell him it was noble!"https://openoldbooks.sgp1.digitaloceanspaces.com/books/dan-merrithew/images/img-184.webpIn the flash of an eye, Dan was making for the assassin.https://openoldbooks.sgp1.digitaloceanspaces.com/books/dan-merrithew/images/img-236.webpOpposite, smiling at him, as though they had breakfasted together for years, was the radiant girl.https://openoldbooks.sgp1.digitaloceanspaces.com/books/dan-merrithew/images/img-front.webpFrontispiece https://openoldbooks.com/books/dan-the-newsboy/read2026-11-15T15:48:14.651Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/dan-the-newsboy/images/i030.webpYou're a couple of swindlers, exclaimed Danhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/dan-the-newsboy/images/cover.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/dan-the-newsboy/images/frontis.webpDAN, THE NEWSBOYhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/dan-the-newsboy/images/logo.webplogohttps://openoldbooks.sgp1.digitaloceanspaces.com/books/dan-the-newsboy/images/i148.webpWhat's the matter with youhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/dan-the-newsboy/images/i266.webpHave you come to take me away https://openoldbooks.com/books/dancers-in-the-dark/read2026-11-15T15:48:14.651Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/dancers-in-the-dark/images/img-cover.webp 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https://openoldbooks.com/books/dancing-devil-range/read2026-11-15T15:48:14.651Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/dancing-devil-range/images/img-001.webpfrontispiecehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/dancing-devil-range/images/img-002.webpguilty-looking man carrying a briefcase 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https://openoldbooks.com/books/danforth-plays-the-game/read2026-11-15T15:48:14.651Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/danforth-plays-the-game/images/i_fp100.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/danforth-plays-the-game/images/i_fp242.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/danforth-plays-the-game/images/i_fp328.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/danforth-plays-the-game/images/cover.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/danforth-plays-the-game/images/i_frontis.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/danforth-plays-the-game/images/logo.webplogo https://openoldbooks.com/books/danger-a-true-history-of-a-great-city-s-wiles-and-temptations-the-veil-lifted-an/read2026-11-15T15:48:14.651Zmonthly0.6 https://openoldbooks.com/books/danger-and-other-stories/read2026-11-15T15:48:14.651Zmonthly0.6 https://openoldbooks.com/books/danger-at-mormon-crossing/read2026-11-15T15:48:14.651Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/danger-at-mormon-crossing/images/pic1.webpLost River Areahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/danger-at-mormon-crossing/images/cover.webpDanger at Mormon Crossing https://openoldbooks.com/books/danger-at-the-drawbridge/read2026-11-15T15:48:14.651Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/danger-at-the-drawbridge/images/cover.webpDanger at the Drawbridgehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/danger-at-the-drawbridge/images/front.webpThe speeding automobile careened down the bank. https://openoldbooks.com/books/danger-cliff-and-other-stories/read2026-11-15T15:48:14.651Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/danger-cliff-and-other-stories/images/image004.webpimage004https://openoldbooks.sgp1.digitaloceanspaces.com/books/danger-cliff-and-other-stories/images/image005.webpimage005https://openoldbooks.sgp1.digitaloceanspaces.com/books/danger-cliff-and-other-stories/images/image006.webpimage006https://openoldbooks.sgp1.digitaloceanspaces.com/books/danger-cliff-and-other-stories/images/image007.webpimage007https://openoldbooks.sgp1.digitaloceanspaces.com/books/danger-cliff-and-other-stories/images/image008.webpimage008https://openoldbooks.sgp1.digitaloceanspaces.com/books/danger-cliff-and-other-stories/images/image009.webpimage009https://openoldbooks.sgp1.digitaloceanspaces.com/books/danger-cliff-and-other-stories/images/image010.webpimage010https://openoldbooks.sgp1.digitaloceanspaces.com/books/danger-cliff-and-other-stories/images/image011.webpimage011https://openoldbooks.sgp1.digitaloceanspaces.com/books/danger-cliff-and-other-stories/images/image013.webpimage013https://openoldbooks.sgp1.digitaloceanspaces.com/books/danger-cliff-and-other-stories/images/image014.webpimage014https://openoldbooks.sgp1.digitaloceanspaces.com/books/danger-cliff-and-other-stories/images/image001.webpimage001https://openoldbooks.sgp1.digitaloceanspaces.com/books/danger-cliff-and-other-stories/images/image002.webpimage002https://openoldbooks.sgp1.digitaloceanspaces.com/books/danger-cliff-and-other-stories/images/image003.webpimage003https://openoldbooks.sgp1.digitaloceanspaces.com/books/danger-cliff-and-other-stories/images/image012.webpimage012 https://openoldbooks.com/books/danger-in-deep-space/read2026-11-15T15:48:14.651Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/danger-in-deep-space/images/img001.webpFrontispiece: Two space cadets, one in space a ship the other on an alien moon with a shovel.https://openoldbooks.sgp1.digitaloceanspaces.com/books/danger-in-deep-space/images/img002.webpSPACE ACADEMY U S Ahttps://openoldbooks.sgp1.digitaloceanspaces.com/books/danger-in-deep-space/images/img003.webpA ringed planethttps://openoldbooks.sgp1.digitaloceanspaces.com/books/danger-in-deep-space/images/img004.webpThe three weary cadets assembled on the control deckhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/danger-in-deep-space/images/img005.webpSpaceman in foreground, rocket in backgroundhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/danger-in-deep-space/images/img006.webpThe junior spaceman maneuvered the great rocket ship toward the air lockhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/danger-in-deep-space/images/img007.webpTom watching the giant teleceiver as a huge star cluster flasheshttps://openoldbooks.sgp1.digitaloceanspaces.com/books/danger-in-deep-space/images/img008.webpSpaceman aiming a devicehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/danger-in-deep-space/images/img009.webpThe jet cab raced along the highway to Venusporthttps://openoldbooks.sgp1.digitaloceanspaces.com/books/danger-in-deep-space/images/img010.webpSpaceship flying over a rocky planethttps://openoldbooks.sgp1.digitaloceanspaces.com/books/danger-in-deep-space/images/img011.webpBangs on floor, Mason and Loring at control boardhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/danger-in-deep-space/images/img012.webpJardine on floorhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/danger-in-deep-space/images/img014.webpTom could see two space-suited figures floating effortlesslyhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/danger-in-deep-space/images/img015.webpSuited spaceman on alien planethttps://openoldbooks.sgp1.digitaloceanspaces.com/books/danger-in-deep-space/images/img016.webpDinosaurs in Venus jungle and tail end of rockethttps://openoldbooks.sgp1.digitaloceanspaces.com/books/danger-in-deep-space/images/img017.webpFront end of rocket in Venus junglehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/danger-in-deep-space/images/img019.webpExplosion near Polarishttps://openoldbooks.sgp1.digitaloceanspaces.com/books/danger-in-deep-space/images/img020.webpMason was frozen into a rigid statue, unable to movehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/danger-in-deep-space/images/img021.webpConnel, Roger, Alfie, and Shinnyhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/danger-in-deep-space/images/img022.webpConnel and Tomhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/danger-in-deep-space/images/img023.webp"Remember," Astro cautioned, "set the fuse for two hours."https://openoldbooks.sgp1.digitaloceanspaces.com/books/danger-in-deep-space/images/img024.webpRoger standing over an unconscious Loringhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/danger-in-deep-space/images/img025.webpAlien creaturehttps://openoldbooks.sgp1.digitaloceanspaces.com/books/danger-in-deep-space/images/img026.webpRocket flying over rocky moonhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/danger-in-deep-space/images/img027.webpRocky moonhttps://openoldbooks.sgp1.digitaloceanspaces.com/books/danger-in-deep-space/images/img028.webp"I know we're going to be sent to the prison asteroid and we deserve it," said Loring.https://openoldbooks.sgp1.digitaloceanspaces.com/books/danger-in-deep-space/images/bc3.webpBook Cover https://openoldbooks.com/books/danger-in-the-void/read2026-11-15T15:48:14.651Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/danger-in-the-void/images/illus.webp https://openoldbooks.com/books/danger-or-wounded-in-the-house-of-a-friend/read2026-11-15T15:48:14.651Zmonthly0.6 https://openoldbooks.com/books/danger-signals/read2026-11-15T15:48:14.651Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/danger-signals/images/p2-190.webp"Are you not doing it just because I am a woman?"https://openoldbooks.sgp1.digitaloceanspaces.com/books/danger-signals/images/p2-219.webp"... Dennis, lying under the telegraph line, his left hand still grasped the instrument"https://openoldbooks.sgp1.digitaloceanspaces.com/books/danger-signals/images/p1-070.webp"It was a strange courting ... there on that engine."https://openoldbooks.sgp1.digitaloceanspaces.com/books/danger-signals/images/p1-100.webp"We carried him into the depot."https://openoldbooks.sgp1.digitaloceanspaces.com/books/danger-signals/images/p1-176.webp"He was the first man I ever killed."https://openoldbooks.sgp1.digitaloceanspaces.com/books/danger-signals/images/p1-236.webp"'Mexican,' said I."https://openoldbooks.sgp1.digitaloceanspaces.com/books/danger-signals/images/p2-016.webp"Two of the men tied my hands in front of me."https://openoldbooks.sgp1.digitaloceanspaces.com/books/danger-signals/images/p2-030.webp"After many efforts I finally reached the lowest cross-arm."https://openoldbooks.sgp1.digitaloceanspaces.com/books/danger-signals/images/p2-038.webp"One of them picked up the lantern, and swaggering over to where I sat all trembling...."https://openoldbooks.sgp1.digitaloceanspaces.com/books/danger-signals/images/p2-100.webp"He looked at me ... then catching me by the collar...."https://openoldbooks.sgp1.digitaloceanspaces.com/books/danger-signals/images/p2-128.webp"... Half lying on the table, face downward, dead by his own hand"https://openoldbooks.sgp1.digitaloceanspaces.com/books/danger-signals/images/p2-144.webp"See here, who is going to pull this train?"https://openoldbooks.sgp1.digitaloceanspaces.com/books/danger-signals/images/p1-fpc.webp"Quick as a flash the Kid had my arm."https://openoldbooks.sgp1.digitaloceanspaces.com/books/danger-signals/images/p1-022.webp"I noticed his long, slim hand on the top of the reverse-lever."https://openoldbooks.sgp1.digitaloceanspaces.com/books/danger-signals/images/p1-282.webp"What seemed to be a giant iceberg...."https://openoldbooks.sgp1.digitaloceanspaces.com/books/danger-signals/images/p1-292.webp"A white city ... was visible for an instant."https://openoldbooks.sgp1.digitaloceanspaces.com/books/danger-signals/images/p2-001.webpFacsimile Of A Completed Order As Entered In The Despatcher@#39;s Order-Book https://openoldbooks.com/books/dangerous-ages/read2026-11-15T15:48:14.651Zmonthly0.6 https://openoldbooks.com/books/dangerous-connections/read2026-11-15T15:48:14.651Zmonthly0.6 https://openoldbooks.com/books/dangerous-days/read2026-11-15T15:48:14.651Zmonthly0.6 https://openoldbooks.com/books/dangerous-deeds/read2026-11-15T15:48:14.651Zmonthly0.6https://openoldbooks.sgp1.digitaloceanspaces.com/books/dangerous-deeds/images/illus-fpc.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/dangerous-deeds/images/illus-emb.webphttps://openoldbooks.sgp1.digitaloceanspaces.com/books/dangerous-deeds/images/saafield.webp