The Mathematical Principles of Natural Philosophy (1846)

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

NEWTON'S PRINCIPIA.

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.

NEW-YORK ·

PUBLISHED BY DANIEL ADEE, 45 LIBERTY STREET.

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

This work was published before January 1, 1927, and is in the public domain worldwide because the author died at least 100 years ago.

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