The Mathematical Principles of Natural Philosophy (1729)
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Contents  

Front Matter  
page  
Title Page  i 
Dedication  iii 
The Author's Preface  vii 
The Preface of Mr Roger Cotes  xiv 
Definitions  1 
9  
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 IIX (Force of gravity)  213 
Propositions XXXIV (Motions of the sea)  230 
Propositions XXVXXXIII (Motions of the moon)  262 
Propositions XXXVIXXXVIII (Forces to move the sea)  305 
Lemmas IIII, Proposition XXXIX (Precession of equinoxes)  315 
Lemmas IVXI, Propositions XLXLII (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]

 THE MOTION OF BODIES
 Of the method of first and last ratios of quantities, by the help whereof we demonstrate the propositions that follow [1]
 Of the invention of centripetal forces [2]
 Of the motion of bodies in eccentric Conic sections [3]
 Of the finding of elliptic, parabolic, and hyperbolic orbits, from the focus given [4]
 How the orbits are to be found when neither focus is given [5]
 How the motions are to be found in given orbits [6]
 Concerning the rectilinear ascent and descent of bodies [7]
 Of the invention of orbits wherein bodies will revolve, being acted upon by any sort of centripetal force [8]
 Of the motion of bodies in movable orbits; and of the motion of the apsides [9]
 Of the motion of bodies in given superficies; and of the reciprocal motion of funependulous bodies [10]
 Of the motions of bodies tending to each other with centripetal forces [11]
 Of the attractive forces of sphaerical bodies [12]
 Of the attractive forces of bodies which are not of a sphaerical figure [13]
 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)
 Of the Motion of Bodies that are resisted in the ratio of the Velocity [15]
 Of the Motion of Bodies that are resisted in the duplicate ratio of their Velocities [16]
 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]
 Of the circular motion of bodies in resisting mediums [18]
 Of the density and compression of fluids; and of Hydrostatics [19]
 Of the motion and resistance of funependulous bodies [20]
 Of the motion of fluids and the resistance made to projected bodies [21]
 Of motion propagated thro' fluids [22]
 Of the circular motion of fluids [23]
Book 3[edit]

 OF THE SYSTEM OF THE WORLD
 Preface to Book 3 [24]
 Rules of Reasoning in Philosophy [25]
 The Phaenomena or Appearances [26]
 Propositions [27]

 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 2535: (disturbances of the motions of the Moon) [40]
 Proposition 3637: (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]
 General Scholium^{[1]} [45]
References (not part of original work)[edit]
 ↑ 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. 223274.". Retrieved 20081119.
This is a translation and has a separate copyright status from the original text. The license for the translation applies to this edition only.
Original: 
This work was published before January 1, 1923, and is in the public domain worldwide because the author died at least 100 years ago. 
Translation: 
This work was published before January 1, 1923, and is in the public domain worldwide because the author died at least 100 years ago. 