The Mathematical Principles of Natural Philosophy (1729)

by Isaac Newton

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

THE

MATHEMATICAL

P R I N C I P L E S

OF

Natural Philosophy.

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By Sir ISAAC NEWTON.

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Translated into English by Andrew Motte.

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To which are added,

The Laws of the MOON's Motion, according
to Gravity.

By John Machin Astron. Prof. Gress. and
Secr. R. Soc.

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In Two Volumes

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LONDON:

Printed for Benjamin Motte, at the Middle-
Temple-Gate, in Fleetstreet.

MDCCXXIX.

Chapters (not listed in original)

Contents
Front Matter
	page
Title Page	i
Dedication	iii
The Author's Preface	vii
The Preface of Mr Roger Cotes	xiv
Definitions	1
Scholium	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 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

THE MOTION OF BODIES

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

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

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 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]

• General Scholium