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
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 [45]

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 published before January 1, 1923 is in the public domain worldwide because the author died at least 100 years ago.
Translation:	This work published before January 1, 1923 is in the public domain worldwide because the author died at least 100 years ago.