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certainly in Babylonia and probably in Egypt, which made the prediction of lunar eclipses fairly reliable, but not of solar eclipses, since those were not always visible at a given spot. We owe to the Babylonians the division of the right angle into ninety degrees, and of the degree into sixty minutes; they had a liking for the number sixty, and even a system of numeration based upon it. The Greeks were fond of attributing the wisdom of their pioneers to travels in Egypt, but what had really been achieved before the Greeks was very little. The prediction of an eclipse by Thales was, however, an example of foreign influence; there is no reason to suppose that he added anything to what he learnt from Egyptian or Babylonian sources, and it was a stroke of luck that his prediction was verified.

Let us begin with some of the earliest discoveries and correct hypotheses. Anaximander thought that the earth floats freely, and is not supported on anything. Aristotle,2 who often rejected the best hypotheses of his time, objected to the theory of Anaximander, that the earth, being at the centre, remained immovable because there was no reason for moving in one direction rather than another. If this were valid, he said, a man placed at the centre of a circle with food at various points of the circumference would starve to death for lack of reason to choose one portion of food rather than another. This argument reappears in scholastic philosophy, not in connection with astronomy, but with free will. It reappears in the form of 'Buridan's ass', which was unable to choose between two bundles of hay placed at equal distances to right and left, and therefore died of hunger.

Pythagoras, in all probability, was the first to think the earth spherical, but his reasons were (one must suppose) aesthetic rather than scientific. Scientific reasons, however, were soon found. Anaxagoras discovered that the moon shines by reflected light, and gave the right theory of eclipses. He himself still thought the earth flat, but the shape of the earth's shadow in lunar eclipses gave the Pythagoreans conclusive arguments in favour of its being spherical. They went further, and regarded the earth as one of the planets. They knew—from Pythagoras himself, it is said—that the morning star and the evening star are identical, and they thought that all the planets, including the earth, move in circles, not round the sun, but round the 'central fire'. They had discovered that the moon always turns the same face to the earth, and they thought that the earth always turns the same face to the 'central fire'. The Mediterranean regions were on the side turned away from the central fire, which was therefore always invisible. The central fire was called 'the house of Zeus', or 'the Mother of the gods'. The sun was supposed to shine by light reflected from the central fire. In addition to the earth, there was another body, the counter-earth, at the same distance from the central fire. For this, they had two reasons, one scientific, one derived from their arithmetical mysticism. The scientific reason was the correct observation that an eclipse of the moon sometimes occurs when both sun and moon are above the horizon. Refraction, which is the cause of this phenomenon, was unknown to them, and they thought that, in such cases, the eclipse must be due to the shadow of a body other than the earth. The other reason was that the sun and moon, the five planets, the earth and counter-earth, and the central fire, made ten heavenly bodies, and ten was the mystic number of the Pythagoreans.

This Pythagorean theory is attributed to Philolaus, a Theban, who lived at the end of the fifth century B.C. Although it is fanciful and in part quite unscientific, it is very important, since it involves the greater part of the

imaginative effort required for conceiving the Copernican hypothesis. To conceive of the earth, not as the centre of the universe, but as one among the planets, not as eternally fixed, but as wandering through space, showed an extraordinary emancipation from anthropocentric