Archimedes Psammites (SandReckoner). Translation from Heath (1932). Aristarchus' heliocentric theory is discussed at length in Heath (1913), but Wall (1975) is of the opinion that Heath has made rather too many assumptions and that there is no evidence that Aristarchus ever wrote a treatise on his heliocentric hypothesis. Indeed, it is very likely that all known references to Aristarchus' theory are derived from this one remark of Archimedes.

Fig. 2.6. Stellar parallax. E\ and E2 are two points on the orbit of the Earth.

The earliest complete astronomical treatise that has survived from ancient Greece is Aristarchus' On the Sizes and Distances of the Sun and Moon. The organization of the work, starting with axioms and then making logical deductions from them, is similar to that of the great contemporary works in geometry such as Euclid's Elements. The treatise is based on six hypotheses:

(i) The Moon receives its light from the Sun.

(ii) The Earth is positioned at the centre of the sphere in which the Moon moves.

(iii) When the Moon appears to us halved, the great circle which divides the dark and bright portions of the Moon is in the direction of our eye.

(iv) When the Moon appears to us halved, its angular distance from the Sun is 87°. (This value is considerably in error. The true value is about 89° 50'.)

(v) The breadth of the Earth's shadow is that of two Moons. (This figure presumably was based on the length of lunar eclipses. The correct figure is nearer three lunar diameters.)

(vi) The Moon has an angular diameter of 2°. (About 4 times too large.22)

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