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34 elsewhere, might with advantage have been noted and followed by many of the so-called Aristotelians of the Middle Ages and of the Renaissance.

31. After the time of Aristotle the centre of Greek scientific thought moved to Alexandria. Founded by Alexander the Great (who was for a time a pupil of Aristotle) in 332 B.C., Alexandria was the capital of Egypt during the reigns of the successive Ptolemies. These kings, especially the second of them, surnamed philadelphos, were patrons of learning; they founded the famous Museum, which contained a magnificent library as well as an observatory, and Alexandria soon became the home of a distinguished body of mathematicians and astronomers. During the next five centuries the only astronomers of importance, with the great exception of Hipparchus (§ 37), were Alexandrines.

32. Among the earlier members of the Alexandrine school were Aristarchus of Samos, Aristyllus, and Timocharis, three nearly contemporary astronomers belonging



to the first half of the 3rd century B.C. The views of Aristarchus on the motion of the earth have already been mentioned (§ 24). A treatise of his On the Magnitudes and Distances of the Sun and Moon is still extant: he there gives an extremely ingenious method for ascertaining the comparative distances of the sun and moon. If, in the figure, and  denote respectively the centres of the earth, sun, and moon, the moon evidently appears to an observer at  half full when the angle  is a right angle. If when this is the case the angular distance between the centres of the sun and moon, i.e. the angle, is measured, two angles of the triangle are