# The Mathematical Principles of Natural Philosophy (1729)

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

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

## Contents

### Book 1

THE MOTION OF BODIES

### Book 2

THE MOTION OF BODIES (In resisting mediums)

### Book 3

OF THE SYSTEM OF THE WORLD
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]