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The_Mathematical_Principles_of_Natural_Philosophy_1846

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The Mathematical Principles of Natural Philosophy
Isaac Newton
1846
Exported from Wikisource on July 17, 2023
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, 1928, and is in the public domain worldwide because the author died at least 100 years ago.
DEDICATION.
* * *
TO THE
TEACHERS OF THE NORMAL SCHOOL
OF THE STATE OF NEW-YORK.
Gentlemen:—
A stirring freshness in the air, and ruddy streaks upon the horizon of the moral world betoken the grateful dawning of a new era. The days of a drivelling instruction are departing. With us is the opening promise of a better time, wherein genuine manhood doing its noblest work shall have adequate reward. Teacher is the...
In conclusion, Gentlemen, to you, as the conspicuous leaders in the vast and honourable labour of Educational Reform, and Popular Teaching, the First American Edition of the Principia of Newton—the greatest work of the greatest Teacher—is most respectfully dedicated.
N. W. CHITTENDEN.
INTRODUCTION TO THE AMERICAN EDITION.
That the Principia of Newton should have remained so generally unknown in this country to the present day is a somewhat remarkable fact; because the name of the author, learned with the very elements of science, is revered at every hearth-stone where knowledge and virtue are of chief esteem, while, abroad, in all the h...
True, the Principia has been hitherto inaccessible to popular use. A few copies in Latin, and occasionally one in English may be found in some of our larger libraries, or in the possession of some ardent disciple of the great Master. But a dead language in the one case, and an enormous price in both, particularly in th...
To the teacher and the taught, the scholar and the student, the devotee of Science and the worshipper of Truth, the Principia must ever continue to be of inestimable value. If to educate means, not so much to store the memory with symbols and facts, as to bring forth the faculties of the soul and develope them to the f...
Let the Principia, then, be gladly welcomed into every Hall where a true teacher presides. And they who are guided to the diligent study of this incomparable work, who become strengthened by its reason, assured by its evidence, and enlightened by its truths, and who rise into loving communion with the great and pure sp...
LIFE OF
SIR ISAAC NEWTON.
* * *
Nec fas est proprius mortali attingere Divos.—Halley.
* * *
From the thick darkness of the middle ages man's struggling spirit emerged as in new birth; breaking out of the iron control of that period; growing strong and confident in the tug and din of succeeding conflict and revolution, it bounded forwards and upwards with resistless vigour to the investigation of physical and ...
Sir Isaac Newton, in whom the rising intellect seemed to attain, as it were, to its culminating point, was born on the 25th of December, O. S. 1642—Christmas day—at Woolsthorpe, in the parish of Colsterworth, in Lincolnshire. His father, John Newton, died at the age of thirty-six, and only a few months after his marria...
Beyond the grandfather, Robert Newton, the descent of Sir Isaac cannot with certainty be traced. Two traditions were held in the family: one, that they were of Scotch extraction; the other, that they came originally from Newton, in Lancashire, dwelling, for a time, however, at Westby, county of Lincoln, before the remo...
The widow Newton was left with the simple means of a comfortable subsistence. The Woolsthorpe estate together with small one which she possessed at Sewstern, in Leicestershire, yielded her an income of some eighty pounds; and upon this limited sum, she had to rely chiefly for the support of herself, and the education o...
Great genius is seldom marked by precocious development; and young Isaac, sent, at the usual age, to two day schools at Skillington and Stoke, exhibited no unusual traits of character. In his twelfth year, he was placed at the public school at Grantham, and boarded at the house of Mr. Clark, an apothecary. But even in ...
His peculiar character began now rapidly to unfold itself. Close application grew to be habitual. Observation alternated with reflection. "A sober, silent, thinking lad," yet, the wisest and the kindliest, the indisputable leader of his fellows. Generosity, modesty, and a love of truth distinguished him then as ever af...
May we not discern in these continual efforts—the diligent research, the patient meditation, the aspiring glance, and the energy of discovery—the stirring elements of that wondrous spirit, which, clear, calm, and great, moved, in after years, through deep onward through deep of Nature's mysteries, unlocking her strongh...
Newton had an early and decided taste for drawing. Pictures, taken sometimes from copies, but often from life, and drawn, coloured and framed by himself, ornamented his apartment. He was skilled also, in poetical composition, "excelled in making verses;" some of these were borne in remembrance and repeated, seventy yea...