Aristarchus of Samos, astronomer, is dated by his observation of the summer solstice in 280 bce. He was a pupil of the Peripatetic *Straton (1) of Lampsacus. He is famous as the author of the heliocentric (see geocentricity) hypothesis, that ‘the fixed stars and sun remain unmoved, and that the earth revolves about the sun on the circumference of a circle, the sun lying in the middle of the orbit’ (Archimedes, Sand-reckoner4–5); he also assumed that the earth rotates about its own axis (Plut. De fac.6). His only extant treatise, On the Sizes and Distances of the Sun and Moon, is, however, on the geocentric basis. Starting with six ‘hypotheses’, the treatise has eighteen propositions displaying the author's facility in both geometry and arithmetic. The ratios of sizes and distances which have to be calculated are equivalent to trigonometric ratios, and Aristarchus finds upper and lower limits to their values starting from assumptions equivalent to well-known theorems in geometry. The results are grossly discrepant from reality: this is due not only to Aristarchus' method, which, though mathematically correct, is ill suited for its purpose (see hipparchus (3)), but also to errors in the hypotheses, notoriously a figure of .