The Mathematical Principles of Natural Philosophy (1846)

by Isaac Newton

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

NEWTON'S PRINCIPIA.

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THE

MATHEMATICAL PRINCIPLES

OF

NATURAL PHILOSOPHY,

BY SIR ISAAC NEWTON;

TRANSLATED INTO ENGLISH BY ANDREW MOTTE.

TO WHICH IS ADDED

NEWTON'S SYSTEM OF THE WORLD;

With a Portrait taken from the Bust in the Royal Observatory at Greenwich.

FIRST AMERICAN EDITION, CAREFULLY REVISED AND CORRECTED,

 

WITH A LIFE OF THE AUTHOR, BY N. W. CHITTENDEN, M. A., &c.

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NEW-YORK ·

PUBLISHED BY DANIEL ADEE, 45 LIBERTY STREET.

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Entered according to Act of Congress, in the year 1846, by

DANIEL ADEE.

In the Clerk's Office of the Southern District Court of New-York.

(not individually listed)
Dedication	3
Introduction to the American Edition	5
Life of Sir Isaac Newton	9
The Principia.
The Author's Preface	67
Book I.
Definitions	73
Axioms, or Laws of Motion	83
Of 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	95
Section II: Of the Invention of Centripetal Forces	103
Section III: Of the motion of bodies in eccentric conic sections	116
Section IV: Of the finding of elliptic, parabolic, and hyperbolic orbits, from the focus given	125
Section V: How the orbits are to be found when neither focus is given	131
Section VI: How the motions are to be found in given orbits	153
Section VII: Concerning the rectilinear ascent and descent of bodies	159
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	172
Section X: Of the motion of bodies in given superficies; and of the reciprocal motion of funependulous bodies	182
Section XI: Of the motions of bodies tending to each other with centripetal forces	194
Section XII: Of the attractive forces of sphærical bodies	218
Section XIII: Of the attractive forces of bodies which are not of a sphærical figure	233
Section XIV: Of the motion of very small bodies when agitated by centripetal forces tending to the several parts of any very great body	243
Book II.
Of the Motion of Bodies
Section I: Of the motion of bodies that are resisted in the ratio of the velocity	251
Section II: Of the motion of bodies that are resisted in the duplicate ratio of their velocities	258
Section III: Of the motions of bodies which are resisted partly in the ratio of the velocities, and partly in the duplicate of the same ratio	279
Section IV: Of the circular motion of bodies in resisting mediums	287
Section V: Of the density and compression of fluids; and of hydrostatics	293
Section VI: Of the motion and resistance of funependulous bodies	303
Section VII: Of the motion of fluids and the resistance made to projected bodies	323
Section VIII: Of motion propagated through fluids	356
Section IX: Of the circular motion of fluids	370
Book III.
Book III	383
Rules of Reasoning in Philosophy	384
Phænomena, or Appearances	386
Propositions I-IX (Force of gravity)	390
Propositions X-XXIV (Motions of celestial bodies and the sea)	400
Propositions XXV-XXXIII (Quantity of lunar motions)	419
Propositions XXXVI-XXXVIII (Forces to move the sea)	449
Lemmas I-III, Proposition XXXIX (Precession of equinoxes)	455
Lemmas IV-XI, Propositions XL-XLII (Comets)	460
General Scholium	503
The System of the World.	511
Index to the Principia.	575