# The Mathematical Principles of Natural Philosophy (1729)

 The Mathematical Principles of Natural Philosophy (1729) by Isaac Newton, translated by Andrew Motte
 An English translation by Andrew Motte, based on the 1726 3rd edition of Philosophiae Naturalis Principia Mathematica. Volume 1: Scan index Volume 2: Scan index
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]

## References (not part of original work)

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.