OF

SIR ISAAC NEWTON'S

PRINCIPIA.

BY

HENRY LORD BROUGHAM, F.R.S.

MEMBER OF THE NATIONAL INSTITUTE OF FRANCE, AND OF THE ROYAL ACADEMY OF NAPLES;

AND

E. J. ROUTH, B.A.

FELLOW OF ST. PETER'S COLLEGE, CAMBRIDGE.

LONDON:

LONGMAN, BROWN, GREEN, AND LONGMANS; C. KNIGHT EDINBURGH: A. AND C. BLACK; GLASGOW: R. GRIFFIN.

1855.

187.0.10.

ΤΟ

PROFESSOR THE BARON PLANA,

OF TURIN,

THIS WORK IS INSCRIBED,

AS A SMALL TOKEN OF RESPECT FOR THE GREAT TALENTS AND

PROFOUND LEARNING OF THAT EMINENT

MATHEMATICIAN.

CONTENTS.

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Galileo's

General remarks. Division of the work into Three Books, 1.

State of Physical Astronomy and Dynamics before Sir Isaac

Newton, 2. General law of gradual discovery, ib. Exam-

ples Logarithms, ib. — Fluxions, ib. -- History of this Cal-

culus, 3. Calculus of Variations, 5. Euler, Lagrange,

Bernouilli, Emerson, 7. Copernican Theory, ib.

discoveries, 8. Kepler's laws, ib. Huygens, ib. Borelli,

ib. Hooke, ib. — Halley, ib. Peculiar maturity of the New-

tonian theory as at first delivered, 10. Nothing since sup-

plied to its demonstration which Sir Isaac Newton originally

had left imperfect, ib. note. Three services beside the disco-

very of Gravitation, performed by this work to science, ib.

Prodigious merit, even if gravitation were struck out of it, 11.

Reception of the Principia slow even in England, ib.

Editions, ib. Maclaurin and Voltaire, 12. Difficulty of read-
ing it from its Conciseness and Synthetical form, ib. - Jesuits'
edition, 13. Submission to papal authority, ib. Pius VII.'s
liberality, Sorbonne and Buffon, ib. note.

I.

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Definitions of the Principia, 14. Two remarks on them, ib.-
Early view given of the Great Discovery to which the whole
work leads, 15. Three laws of motion, ib. - Six corollaries

to them, ib.·

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Summary of dynamics, as it existed before Sir
Isaac Newton, 16. Scholium to the laws of motion, upon
uniform and accelerated motion, 17. Laws and formulas on
velocity, space, and time, ib. note.

(SECTION I. Principia.)- Method

19. Treatise on Fluxions, 20.

generation of quantities, ib.

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of prime and ultimate ratios,

- Fundamental principle of the

Generation of curves, 21.