The Mathematical Principles of Natural Philosophy (1729)

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.

By Sir ISAAC NEWTON.

Translated into English by Andrew Motte.

To which are added,

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

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

In Two Volumes

LONDON:

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

MDCCXXIX.

Contents (not listed in original)

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: Of the method of first and last ratios of quantities, by the help whereof we demonstrate the propositions that follow	41
Section II: Of the invention of centripetal forces	57
Section III: Of the motion of bodies in eccentric Conic sections	79
Section IV: Of the finding of elliptic, parabolic, and hyperbolic orbits, from the focus given	94
Section V: How the orbits are to be found when neither focus is given	104
Section VI: How the motions are to be found in given orbits	143
Section VII: Concerning the rectilinear ascent and descent of bodies	154
Section VIII: Of the invention of orbits wherein bodies will revolve, being acted upon by any sort of centripetal force	168
Section IX: Of the motion of bodies in movable orbits; and of the motion of the apsides	177
Section X: Of the motion of bodies in given superficies; and of the reciprocal motion of funependulous bodies	196
Section XI: Of the motions of bodies tending to each other with centripetal forces	218
Section XII: Of the attractive forces of sphaerical bodies	263
Section XIII: Of the attractive forces of bodies which are not of a sphaerical figure	292
Section XIV: Of the motion of very small bodies when agitated by centripetal forces tending to the several parts of any very great body	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

THE MOTION OF BODIES (In resisting mediums)

Of the Motion of Bodies that are resisted in the ratio of the Velocity [1]
Of the Motion of Bodies that are resisted in the duplicate ratio of their Velocities [2]
Of the Motions of Bodies which are resisted partly in the ratio of the Velocities, and partly in the duplicate of the same ratio [3]
Of the circular motion of bodies in resisting mediums [4]
Of the density and compression of fluids; and of Hydrostatics [5]
Of the motion and resistance of funependulous bodies [6]
Of the motion of fluids and the resistance made to projected bodies [7]
Of motion propagated thro' fluids [8]
Of the circular motion of fluids [9]

OF THE SYSTEM OF THE WORLD

Motion of the satellites of Jupiter [14]

Propositions 2: the primary Planets, and 3: the Moon [15]

Proposition 10: Longevity of planetary motions [18]

Proposition 11: Common centre of gravity of the Earth, the Sun and all the Planets [19]

Proposition 13: the Planets move in Ellipses [20]

Proposition 17: the diurnal motions of the Planets are uniform [21]

Proposition 18: (oblateness of the Planets & the Earth) [22]

Proposition 21: the equinoctial points go backwards [23]

Proposition 22: all the motions of the Moon ... follow from the principles ... laid down [24]

Proposition 24: the flux and reflux of the Sea, arise from the actions of the Sun and Moon [25]

Propositions 25-35: (disturbances of the motions of the Moon) [26]

Proposition 36-37: (forces of Sun & Moon to move the Sea) [27]

Proposition 38: Figure of the Moon's Body [28]

Proposition 39: precession of the equinoxes [29]

(Theory of the comets) [30]

This work is a translation and has a separate copyright status to the applicable copyright protections of the original content.

Original:	This work was published before January 1, 1930, and is in the public domain worldwide because the author died at least 100 years ago. Public domainPublic domainfalsefalse
Translation:	This work was published before January 1, 1930, and is in the public domain worldwide because the author died at least 100 years ago. Public domainPublic domainfalsefalse