The Mathematical Principles of Natural Philosophy (1846)

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The Mathematical Principles of Natural Philosophy  (1846) 
by Isaac Newton, translated by Andrew Motte
The first "American" edition of Philosophiae Naturalis Principia Mathematica. Edited by N. W. Chittenden.
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.


Contents[1][edit]

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 sphaerical bodies 218
Section XIII: Of the attractive forces of bodies which are not of a sphaerical 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
Phaenomena, 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

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