The Philosophy of Mathematics, translated by W. M. Gillespie
by Auguste Comte
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Language: English
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About this eBook
- Author
- Comte, Auguste, 1798-1857
- Title
- The philosophy of mathematics
- Credits
- Produced by Anna Hall, Albert László and the Online Distributed Proofreading Team at www.pgdp.net (This file was produced from images generously made available by The Internet Archive)
- Language
- English
- LoC Class
- QA: Science: Mathematics
- Subject
- Mathematics -- Philosophy
- Category
- Text
- eBook-No.
- 39702
- Project Gutenberg
- https://www.gutenberg.org/ebooks/39702
- Release Date
- May 15, 2012
- Copyright
- Public domain in the USA.
Contents
- 1.THE PHILOSOPHY OF MATHEMATICS.
- 2.PREFACE. — ANALYTICAL TABLE OF CONTENTS. — BOOK I. ANALYSIS. — BOOK II. GEOMETRY.
- 3.INTRODUCTION. — THE OBJECT OF MATHEMATICS. — TRUE DEFINITION OF MATHEMATICS. — ITS TWO FUNDAMENTAL DIVISIONS. — CONCRETE MATHEMATICS. — ABSTRACT MATHEMATICS. — THE EXTENT OF ITS FIELD. — ANALYSIS.
- 4.CHAPTER I. — GENERAL VIEW OF MATHEMATICAL ANALYSIS. — THE TRUE IDEA OF AN EQUATION. — THE TWO PRINCIPAL DIVISIONS OF THE CALCULUS. — THE CALCULUS OF VALUES, OR ARITHMETIC. — THE CALCULUS OF FUNCTIONS, OR ALGEBRA.
- 5.CHAPTER II. — ORDINARY ANALYSIS, OR ALGEBRA. — ALGEBRAIC EQUATIONS. — ALGEBRAIC RESOLUTION OF EQUATIONS. — NUMERICAL RESOLUTION OF EQUATIONS. — THE THEORY OF EQUATIONS. — THE METHOD OF INDETERMINATE COEFFICIENTS. — IMAGINARY QUANTITIES. — NEGATIVE QUANTITIES. — PRINCIPLE OF HOMOGENEITY.
- 6.CHAPTER III. — TRANSCENDENTAL ANALYSIS: DIFFERENT MODES OF VIEWING IT. — ITS EARLY HISTORY. — METHOD OF LEIBNITZ. — METHOD OF NEWTON. — METHOD OF LAGRANGE. — FUNDAMENTAL IDENTITY OF THE THREE METHODS. — COMPARATIVE VALUE OF THE THREE METHODS.
- 7.CHAPTER IV. — THE DIFFERENTIAL AND INTEGRAL CALCULUS. ITS TWO FUNDAMENTAL DIVISIONS. — THEIR RELATIONS TO EACH OTHER. — THE DIFFERENTIAL CALCULUS. — THE INTEGRAL CALCULUS.
- 8.CHAPTER V. — THE CALCULUS OF VARIATIONS. — PROBLEMS GIVING RISE TO IT. — METHOD OF LAGRANGE. — ITS RELATIONS TO THE ORDINARY CALCULUS.
- 9.CHAPTER VI. — THE CALCULUS OF FINITE DIFFERENCES. — GENERAL THEORY OF SERIES. — PERIODIC OR DISCONTINUOUS FUNCTIONS. — APPLICATIONS OF THIS CALCULUS. — GEOMETRY.
- 10.CHAPTER I. — GENERAL VIEW OF GEOMETRY. — THE FINAL OBJECT OF GEOMETRY. — INFINITE EXTENT OF ITS FIELD. — EXPANSION OF ORIGINAL DEFINITION. — PROPERTIES OF LINES AND SURFACES. — THE TWO GENERAL METHODS OF GEOMETRY.
- 11.CHAPTER II. — ANCIENT OR SYNTHETIC GEOMETRY. — ITS PROPER EXTENT. — GEOMETRY OF THE RIGHT LINE. — GRAPHICAL SOLUTIONS. — DESCRIPTIVE GEOMETRY. — ALGEBRAIC SOLUTIONS. — TRIGONOMETRY.
- 12.CHAPTER III. — MODERN OR ANALYTICAL GEOMETRY. — ANALYTICAL REPRESENTATION OF FIGURES. — PLANE CURVES. — CHOICE OF CO-ORDINATES. — SURFACES. — CURVES OF DOUBLE CURVATURE. — IMPERFECTIONS OF ANALYTICAL GEOMETRY.
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