A Treatise on Spherical Astronomy

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University Press, 1908 - Spherical astronomy - 506 pages
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Page 147 - Newton generalized the law of attraction into a statement that every particle of matter in the universe attracts every other particle with a force which varies directly as the product of their masses and inversely as the square of the distance between them; and he thence deduced the law of attraction for spherical shells of constant density.
Page 146 - LAW I. Every body continues in its state of rest, or of uniform motion in a straight line, except in so far as it may be compelled to change that state by impressed forces.
Page 299 - The squares of the periodic times of the planets are proportional to the cubes of their mean distances from the sun.
Page 146 - Change of motion is proportional to the impressed force and takes place in the direction of the straight line in which the force acts.
Page 425 - Up to now we have been explaining to the best of our ability the revolutions of the Earth around the sun and of the moon around the Earth.
Page 4 - III., when two sides and an angle opposite to one of them are given...
Page 13 - A cos 6 = cos a cos c + sin a sin c cos B cos c = cos a cos 6 + sin a sin 6 cos C Law of Cosines for Angles cos A = — cos B...
Page 13 - Triangle to equations (I) they become t sin.- A cos. b = cos. B sin. C + sin. B cos. C cos. a ; I sin. A cos. c = cos. C sin. B + sin. C cos. B cos. a. sin. B cos. c = cos. C sin. A + sin. C cos. A cos.
Page 146 - To every action there is always an equal and contrary reaction ; or, the mutual actions of any two bodies are always equal and oppositely directed in the same straight line.
Page 1 - C = cos. c sin. a — sin. c cos. a cos. B ; I sin. b cos. A = cos. a sin. c — sin. a cos. c cos. B. i sin. c cos. A = cos. a sin.

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