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The philosophy of mathematics

By Auguste Comte
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Table of Contents
  • THE PHILOSOPHY OF MATHEMATICS.
    • PREFACE.
      • ANALYTICAL TABLE OF CONTENTS.
        • BOOK I. ANALYSIS.
        • BOOK II. GEOMETRY.
      • BOOK I. ANALYSIS.
      • BOOK II. GEOMETRY.
    • ANALYTICAL TABLE OF CONTENTS.
      • 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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