The Mathematical Principles of Natural Philosophy (1729)

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For other English-language translations of this work, see The Mathematical Principles of Natural Philosophy.
Title page

Front Matter
Title Page i
Dedication iii
The Author's Preface vii
The Preface of Mr Roger Cotes xiv
Definitions 1
Axioms, or Laws of Motion 19
Book 1: The Motion of Bodies
Section I 41
Section II 57
Section III 79
Section IV 94
Section V 104
Section VI 143
Section VII 154
Section VIII 168
Section IX 177
Section X 196
Section XI 218
Section XII 263
Section XIII 292
Section XIV 311
Book 2: The Motion of Bodies (in resisting mediums)
Section I 1
Section II 12
Section III 45
Section IV 55
Section V 64
Section VI 80
Section VII 111
Section VIII 163
Section IX 184
Book 3: Of the System of the World
Rules of Reasoning in Philosophy 202
Phænomena, or Appearances 206
Propositions I-IX (Force of gravity) 213
Propositions X-XXIV (Motions of the sea) 230
Propositions XXV-XXXIII (Motions of the moon) 262
Propositions XXXVI-XXXVIII (Forces to move the sea) 305
Lemmas I-III, Proposition XXXIX (Precession of equinoxes) 315
Lemmas IV-XI, Propositions XL-XLII (Comets) 323
General Scholium 387
Index XX
Appendix i
The Laws of the Moon's Motion according to Gravity (John Machin) (1)
Errata XX

Book 1[edit]

  1. Of the method of first and last ratios of quantities, by the help whereof we demonstrate the propositions that follow [1]
  2. Of the invention of centripetal forces [2]
  3. Of the motion of bodies in eccentric Conic sections [3]
  4. Of the finding of elliptic, parabolic, and hyperbolic orbits, from the focus given [4]
  5. How the orbits are to be found when neither focus is given [5]
  6. How the motions are to be found in given orbits [6]
  7. Concerning the rectilinear ascent and descent of bodies [7]
  8. Of the invention of orbits wherein bodies will revolve, being acted upon by any sort of centripetal force [8]
  9. Of the motion of bodies in movable orbits; and of the motion of the apsides [9]
  10. Of the motion of bodies in given superficies; and of the reciprocal motion of funependulous bodies [10]
  11. Of the motions of bodies tending to each other with centripetal forces [11]
  12. Of the attractive forces of sphaerical bodies [12]
  13. Of the attractive forces of bodies which are not of a sphaerical figure [13]
  14. Of the motion of very small bodies when agitated by centripetal forces tending to the several parts of any very great body [14]

Book 2[edit]

THE MOTION OF BODIES (In resisting mediums)
  1. Of the Motion of Bodies that are resisted in the ratio of the Velocity [15]
  2. Of the Motion of Bodies that are resisted in the duplicate ratio of their Velocities [16]
  3. Of the Motions of Bodies which are resisted partly in the ratio of the Velocities, and partly in the duplicate of the same ratio [17]
  4. Of the circular motion of bodies in resisting mediums [18]
  5. Of the density and compression of fluids; and of Hydrostatics [19]
  6. Of the motion and resistance of funependulous bodies [20]
  7. Of the motion of fluids and the resistance made to projected bodies [21]
  8. Of motion propagated thro' fluids [22]
  9. Of the circular motion of fluids [23]

Book 3[edit]

Motion of the satellites of Jupiter [28]
Propositions 2: the primary Planets, and 3: the Moon [29]
Proposition 6: Gravitation towards every Planet [30]
Proposition 7: Gravity tending to all Bodies [31]
Proposition 10: Longevity of planetary motions [32]
Proposition 11: Common centre of gravity of the Earth, the Sun and all the Planets [33]
Proposition 13: the Planets move in Ellipses [34]
Proposition 17: the diurnal motions of the Planets are uniform [35]
Proposition 18: (oblateness of the Planets & the Earth) [36]
Proposition 21: the equinoctial points go backwards [37]
Proposition 22: all the motions of the Moon ... follow from the principles ... laid down [38]
Proposition 24: the flux and reflux of the Sea, arise from the actions of the Sun and Moon [39]
Propositions 25-35: (disturbances of the motions of the Moon) [40]
Proposition 36-37: (forces of Sun & Moon to move the Sea) [41]
Proposition 38: Figure of the Moon's Body [42]
Proposition 39: precession of the equinoxes [43]
(Theory of the comets) [44]

References (not part of original work)[edit]

  1. Ducheyne, Steffen. "The General Scholium: Some notes on Newton’s published and unpublished endeavours, Lias: Sources and Documents Relating to the Early Modern History of Ideas, vol. 33, n° 2, pp. 223-274.". Retrieved 2008-11-19.