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aberration altitude antinole approximate ascending node assume astronomical axes axis azimuth celestial sphere centre clock constant coordinates corresponding cos2 cosec curve decl determine difference Differentiating direction diurnal diurnal motion earth earth's surface eccentricity ecliptic ellipse ephemeris equal equation equinox error expression follows formula geocentric given graduated great circle Greenwich mean Hence horizon horizontal parallax hour angle intersection interval Kepler's known latitude f logarithms loxodrome Math mean distance mean longitude mean noon mean solar measured meridian moon moon's motion nole nutation obliquity observer obtain parallel perpendicular planet point of Aries position angle precession proper motion quantities radius vector refraction respectively right ascension rotation seconds of arc sidereal day sin2 sine solstice spherical triangle star stereographic projection substitution sun's supposed tan2 tangent true true anomaly velocity whence zenith distance zero
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 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.