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36 positions on the sky; they may thus be regarded as the authors of the first real star catalogue, earlier astronomers having only attempted to fix the position of the stars by more or less vague verbal descriptions. They also made a number of valuable observations of the planets, the sun, etc., of which succeeding astronomers, notably Hipparchus and Ptolemy, were able to make good use.

33. Among the important contributions of the Greeks to astronomy must be placed the development, chiefly from the mathematical point of view, of the consequences of the rotation of the celestial sphere and of some of the simpler motions of the celestial bodies, a development the individual steps of which it is difficult to trace. We have,



however, a series of minor treatises or textbooks, written for the most part during the Alexandrine period, dealing with this branch of the subject (known generally as Spherics, or the Doctrine of the Sphere), of which the Phenomena of the famous geometer Euclid (about 300 B.C.) is a good example. In addition to the points and circles of the sphere already mentioned (chapter, §§ 8–11), we now find explicitly recognised the horizon, or the great circle in which a horizontal plane through the observer meets the celestial sphere, and its pole, the zenith, or