Library

Mathematical Principles of Natural Philosophy

Isaac Newton

Andrew Motte (1846)

Isaac Newton's Philosophiæ Naturalis Principia Mathematica (1687) is the founding work of classical mechanics and one of the most consequential books in the history of science. Proceeding from the Definitions and the three Axioms or Laws of Motion, Book I develops the mathematics of motion under central forces and the geometry of conic-section orbits; Book II treats the motion of bodies in resisting media; and Book III, 'The System of the World,' applies the whole apparatus to the cosmos, deriving universal gravitation and the motions of the planets, moon, tides, and comets. The rendering is Andrew Motte's of 1729, the first and long-standard English translation.

Start readingYour notebookShow in graph

Contents

1. Author's Preface
2. Definitions
3. Axioms, or Laws of Motion
4. Book I, Section I
   1. Lemma I
   2. Lemma II
   3. Lemma III
   4. Lemma IV
   5. Lemma V
   6. Lemma VI
   7. Lemma VII
   8. Lemma VIII
   9. Lemma IX
   10. Lemma X
   11. Lemma XI
5. Book I, Section II
   1. Proposition I
   2. Proposition II
   3. Proposition III
   4. Proposition IV
   5. Proposition V
   6. Proposition VI
   7. Proposition VII
   8. Proposition VIII
   9. Proposition IX
   10. Lemma XII
   11. Proposition X
6. Book I, Section III
   1. Proposition XI
   2. Proposition XII
   3. Lemma XIII
   4. Lemma XIV
   5. Proposition XIII
   6. Proposition XIV
   7. Proposition XV
   8. Proposition XVI
   9. Proposition XVII
7. Book I, Section IV
   1. Lemma XV
   2. Proposition XVIII
   3. Proposition XIX
   4. Proposition XX
   5. Lemma XVI
   6. Proposition XXI
8. Book I, Section V
   1. Lemma XVII
   2. Lemma XVIII
   3. Lemma XIX
   4. Lemma XX
   5. Lemma XXI
   6. Proposition XXII
   7. Proposition XXIII
   8. Proposition XXIV
   9. Lemma XXII
   10. Proposition XXV
   11. Proposition XXVI
   12. Lemma XXIII
   13. Lemma XXIV
   14. Lemma XXV
   15. Proposition XXVII
   16. Lemma XXVI
   17. Proposition XXVIII
   18. Lemma XXVII
   19. Proposition XXIX
9. Book I, Section VI
   1. Proposition XXX
   2. Lemma XXVIII
   3. Proposition XXXI
10. Book I, Section VII
    1. Proposition XXXII
    2. Proposition XXXIII
    3. Proposition XXXIV
    4. Proposition XXXV
    5. Proposition XXXVI
    6. Proposition XXXVII
    7. Proposition XXXVIII
    8. Proposition XXXIX
11. Book I, Section VIII
    1. Proposition XL
    2. Proposition XLI
    3. Proposition XLII
12. Book I, Section IX
    1. Proposition XLIII
    2. Proposition XLIV
    3. Proposition XLV
13. Book I, Section X
    1. Proposition XLVI
    2. Proposition XLVII
    3. Proposition XLVIII
    4. Proposition XLIX
    5. Proposition L
    6. Proposition LI
    7. Proposition LII
    8. Proposition LIII
    9. Proposition LIV
    10. Proposition LV
    11. Proposition LVI
14. Book I, Section XI
    1. Proposition LVII
    2. Proposition LVIII
    3. Proposition LIX
    4. Proposition LX
    5. Proposition LXI
    6. Proposition LXII
    7. Proposition LXIII
    8. Proposition LXIV
    9. Proposition LXV
    10. Proposition LXVI
    11. Proposition LXVII
    12. Proposition LXVIII
    13. Proposition LXIX
15. Book I, Section XII
    1. Proposition LXX
    2. Proposition LXXI
    3. Proposition LXXII
    4. Proposition LXXIII
    5. Proposition LXXIV
    6. Proposition LXXV
    7. Proposition LXXVI
    8. Proposition LXXVII
    9. Proposition LXXVIII
    10. Lemma XXIX
    11. Proposition LXXIX
    12. Proposition LXXX
    13. Proposition LXXXI
    14. Proposition LXXXII
    15. Proposition LXXXIII
    16. Proposition LXXXIV
16. Book I, Section XIII
    1. Proposition LXXXV
    2. Proposition LXXXVI
    3. Proposition LXXXVII
    4. Proposition LXXXVIII
    5. Proposition LXXXIX
    6. Proposition XC
    7. Proposition XCI
    8. Proposition XCII
    9. Proposition XCIII
17. Book I, Section XIV
    1. Proposition XCIV
    2. Proposition XCV
    3. Proposition XCVI
    4. Proposition XCVII
    5. Proposition XCVIII
18. Book II, Section I
    1. Proposition I
    2. Lemma I
    3. Proposition II
    4. Proposition III
    5. Proposition IV
19. Book II, Section II
    1. Proposition V
    2. Proposition VI
    3. Proposition VII
    4. Lemma II
    5. Proposition VIII
    6. Proposition IX
    7. Proposition X
20. Book II, Section III
    1. Proposition XI
    2. Proposition XII
    3. Proposition XIII
    4. Proposition XIV
21. Book II, Section IV
    1. Lemma III
    2. Proposition XV
    3. Proposition XVI
    4. Proposition XVII
    5. Proposition XVIII
22. Book II, Section V
    1. Proposition XIX
    2. Proposition XX
    3. Proposition XXI
    4. Proposition XXII
    5. Proposition XXIII
23. Book II, Section VI
    1. Proposition XXIV
    2. Proposition XXV
    3. Proposition XXVI
    4. Proposition XXVII
    5. Proposition XXVIII
    6. Proposition XXIX
    7. Proposition XXX
    8. Proposition XXXI
24. Book II, Section VII
    1. Proposition XXXII
    2. Proposition XXXIII
    3. Proposition XXXIV
    4. Proposition XXXV
    5. Proposition XXXVI
    6. Lemma IV
    7. Proposition XXXVII
    8. Lemma V
    9. Lemma VI
    10. Lemma VII
    11. Proposition XXXVIII
    12. Proposition XXXIX
    13. Proposition XL
25. Book II, Section VIII
    1. Proposition XLI
    2. Proposition XLII
    3. Proposition XLIII
    4. Proposition XLIV
    5. Proposition XLV
    6. Proposition XLVI
    7. Proposition XLVII
    8. Proposition XLVIII
    9. Proposition XLIX
    10. Proposition L
26. Book II, Section IX
    1. Proposition LI
    2. Proposition LII
    3. Proposition LIII
27. Book III
    1. Proposition I
    2. Proposition II
    3. Proposition III
    4. Proposition IV
    5. Proposition V
    6. Proposition VI
    7. Proposition VII
    8. Proposition VIII
    9. Proposition IX
    10. Proposition X
    11. Proposition XI
    12. Proposition XII
    13. Proposition XIII
    14. Proposition XIV
    15. Proposition XV
    16. Proposition XVI
    17. Proposition XVII
    18. Proposition XVIII
    19. Proposition XIX
    20. Proposition XX
    21. Proposition XXI
    22. Proposition XXII
    23. Proposition XXIII
    24. Proposition XXIV
    25. Proposition XXV
    26. Proposition XXVI
    27. Proposition XXVII
    28. Proposition XXVIII
    29. Proposition XXIX
    30. Proposition XXX
    31. Proposition XXXI
    32. Proposition XXXII
    33. Proposition XXXIII
    34. Proposition I
    35. Proposition II
    36. Proposition XXXIV
    37. Proposition XXXV
    38. Proposition XXXVI
    39. Proposition XXXVII
    40. Proposition XXXVIII
    41. Lemma I
    42. Lemma II
    43. Lemma III
    44. Proposition XXXIX
    45. Lemma IV
    46. Proposition XL
    47. Lemma V
    48. Lemma VI
    49. Lemma VII
    50. Lemma VIII
    51. Lemma IX
    52. Lemma X
    53. Lemma XI
    54. Proposition XLI
    55. Proposition XLII
    56. General Scholium