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Book

The philosophy of mathematics

by Auguste Comte (1798–1857)

Portrait of Auguste Comte
Johan Hendrik Hoffmeister · Public domain

61 chapters, about 60,000 words. The text is in the public domain in the United States and comes from Project Gutenberg.

Chapters

  1. MATHEMATICS. 200 words
  2. PREFACE. 900 words
  3. GENERAL CONSIDERATIONS. 400 words
  4. THE OBJECT OF MATHEMATICS. 1,800 words
  5. TRUE DEFINITION OF MATHEMATICS. 400 words
  6. ITS TWO FUNDAMENTAL DIVISIONS. 1,400 words
  7. CONCRETE MATHEMATICS. 400 words
  8. ABSTRACT MATHEMATICS. 600 words
  9. THE EXTENT OF ITS FIELD. 1,500 words
  10. GENERAL VIEW OF MATHEMATICAL ANALYSIS. 400 words
  11. THE TRUE IDEA OF AN EQUATION. 900 words
  12. FUNCTION. ITS NAME. 700 words
  13. THE TWO PRINCIPAL DIVISIONS OF THE CALCULUS. 700 words
  14. THE CALCULUS OF VALUES, OR ARITHMETIC. 1,200 words
  15. THE CALCULUS OF FUNCTIONS, OR ALGEBRA. 1,800 words
  16. ORDINARY ANALYSIS, OR ALGEBRA. 500 words
  17. ALGEBRAIC EQUATIONS. 300 words
  18. ALGEBRAIC RESOLUTION OF EQUATIONS. 800 words
  19. NUMERICAL RESOLUTION OF EQUATIONS. 1,100 words
  20. THE THEORY OF EQUATIONS. 100 words
  21. THE METHOD OF INDETERMINATE COEFFICIENTS. 200 words
  22. IMAGINARY QUANTITIES. 200 words
  23. NEGATIVE QUANTITIES. 600 words
  24. PRINCIPLE OF HOMOGENEITY. 900 words
  25. DIFFERENT MODES OF VIEWING IT. 300 words
  26. ITS EARLY HISTORY. 600 words
  27. METHOD OF LEIBNITZ. 2,400 words
  28. METHOD OF NEWTON. 1,200 words
  29. METHOD OF LAGRANGE. 300 words
  30. FUNDAMENTAL IDENTITY OF THE THREE METHODS. 800 words
  31. COMPARATIVE VALUE OF THE THREE METHODS. 1,600 words
  32. ITS TWO FUNDAMENTAL DIVISIONS. 300 words
  33. THEIR RELATIONS TO EACH OTHER. 1,000 words
  34. THE DIFFERENTIAL CALCULUS. 2,100 words
  35. THE INTEGRAL CALCULUS. 4,400 words
  36. PROBLEMS GIVING RISE TO IT. 900 words
  37. METHOD OF LAGRANGE. 2,100 words
  38. ITS RELATIONS TO THE ORDINARY CALCULUS. 700 words
  39. THE CALCULUS OF FINITE DIFFERENCES. 600 words
  40. GENERAL THEORY OF SERIES. 800 words
  41. PERIODIC OR DISCONTINUOUS FUNCTIONS. 100 words
  42. APPLICATIONS OF THIS CALCULUS. 500 words
  43. GENERAL VIEW OF GEOMETRY. 1,400 words
  44. THE FINAL OBJECT OF GEOMETRY. 1,500 words
  45. INFINITE EXTENT OF ITS FIELD. 1,000 words
  46. EXPANSION OF ORIGINAL DEFINITION. 300 words
  47. PROPERTIES OF LINES AND SURFACES. 2,100 words
  48. THE TWO GENERAL METHODS OF GEOMETRY. 2,500 words
  49. ITS PROPER EXTENT. 1,400 words
  50. GEOMETRY OF THE RIGHT LINE. 100 words
  51. GRAPHICAL SOLUTIONS. 600 words
  52. DESCRIPTIVE GEOMETRY. 1,000 words
  53. ALGEBRAIC SOLUTIONS. 200 words
  54. TRIGONOMETRY. 1,800 words
  55. MODERN OR ANALYTICAL GEOMETRY. 100 words
  56. ANALYTICAL REPRESENTATION OF FIGURES. 1,200 words
  57. PLANE CURVES. 2,400 words
  58. CHOICE OF CO-ORDINATES. 1,700 words
  59. SURFACES. 1,000 words
  60. CURVES OF DOUBLE CURVATURE. 800 words
  61. IMPERFECTIONS OF ANALYTICAL GEOMETRY. 200 words

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