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# The philosophy of mathematics

By Auguste Comte
Free
Book Description
• THE PHILOSOPHY OF MATHEMATICS.
• PREFACE.
• BOOK I. ANALYSIS.
• BOOK II. GEOMETRY.
• BOOK I. ANALYSIS.
• BOOK II. GEOMETRY.
• BOOK I. ANALYSIS.
• BOOK II. GEOMETRY.
• BOOK I. ANALYSIS.
• BOOK II. GEOMETRY.
• INTRODUCTION.
• THE OBJECT OF MATHEMATICS.
• TRUE DEFINITION OF MATHEMATICS.
• ITS TWO FUNDAMENTAL DIVISIONS.
• CONCRETE MATHEMATICS.
• ABSTRACT MATHEMATICS.
• THE EXTENT OF ITS FIELD.
• THE OBJECT OF MATHEMATICS.
• TRUE DEFINITION OF MATHEMATICS.
• ITS TWO FUNDAMENTAL DIVISIONS.
• CONCRETE MATHEMATICS.
• ABSTRACT MATHEMATICS.
• THE EXTENT OF ITS FIELD.
• ANALYSIS.
• 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.
• 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.
• 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.
• 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.
• 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.
• 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.
• CHAPTER IV.
• THE DIFFERENTIAL AND INTEGRAL CALCULUS. ITS TWO FUNDAMENTAL DIVISIONS.
• THEIR RELATIONS TO EACH OTHER.
• THE DIFFERENTIAL CALCULUS.
• THE INTEGRAL CALCULUS.
• THE DIFFERENTIAL AND INTEGRAL CALCULUS. ITS TWO FUNDAMENTAL DIVISIONS.
• THEIR RELATIONS TO EACH OTHER.
• THE DIFFERENTIAL CALCULUS.
• THE INTEGRAL CALCULUS.
• CHAPTER V.
• THE CALCULUS OF VARIATIONS.
• PROBLEMS GIVING RISE TO IT.
• METHOD OF LAGRANGE.
• ITS RELATIONS TO THE ORDINARY CALCULUS.
• THE CALCULUS OF VARIATIONS.
• PROBLEMS GIVING RISE TO IT.
• METHOD OF LAGRANGE.
• ITS RELATIONS TO THE ORDINARY CALCULUS.
• CHAPTER VI.
• THE CALCULUS OF FINITE DIFFERENCES.
• GENERAL THEORY OF SERIES.
• PERIODIC OR DISCONTINUOUS FUNCTIONS.
• APPLICATIONS OF THIS CALCULUS.
• THE CALCULUS OF FINITE DIFFERENCES.
• GENERAL THEORY OF SERIES.
• PERIODIC OR DISCONTINUOUS FUNCTIONS.
• APPLICATIONS OF THIS CALCULUS.
• GEOMETRY.
• 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.
• 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.
• CHAPTER II.
• ANCIENT OR SYNTHETIC GEOMETRY.
• ITS PROPER EXTENT.
• GEOMETRY OF THE RIGHT LINE.
• GRAPHICAL SOLUTIONS.
• DESCRIPTIVE GEOMETRY.
• ALGEBRAIC SOLUTIONS.
• TRIGONOMETRY.
• ANCIENT OR SYNTHETIC GEOMETRY.
• ITS PROPER EXTENT.
• GEOMETRY OF THE RIGHT LINE.
• GRAPHICAL SOLUTIONS.
• DESCRIPTIVE GEOMETRY.
• ALGEBRAIC SOLUTIONS.
• TRIGONOMETRY.
• 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.
• 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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