S. Anatolius Alexandrinus, Fragmenta ex libris arithmeticis (ut videtur)

or even in many ways. In one way it is the dramatic reversal of fortune, according to which there are said to be plots of the dramas of Euripides. According to another signification it is the investigation of particular cases in rhetoric, according to which the sophists say that a hypothesis must be laid down. And according to a third sense a hypothesis is called the starting-point of demonstration, being a postulate of things for the establishment of something. Thus Democritus is said to use atoms and void as a hypothesis, and Asclepiades corpuscles and pores. Mathematics, therefore, is occupied with the third.

That not only Pythagoras honoured arithmetic, but also his disciples, saying in addition: ". . . and all things resemble number."

That arithmetic has as its consequent end, properly speaking, scientific contemplation, than which no end is either greater or fairer; and secondarily, to comprehend summarily how many properties belong to determinate being.

Who discovered what in mathematics? Eudemus relates in his Astrologies that Oenopides first discovered the obliquity of the zodiac and the revolution of the Great Year; Thales the eclipse of the sun and its period according to the solstices, how it does not always turn out equal; Anaximander that the earth is suspended in mid-air and moves about the centre of the cosmos; Anaximenes that the moon has its light from the sun and in what manner it is eclipsed. And the rest added other things to these discoveries.

That the fixed stars move about the axis through the poles which remains stationary, whereas the planets move about the axis of the zodiac which is at right angles to it, and are distant from one another; that the axes of the fixed stars and of the planets are the side of a fifteen-sided figure, which is twenty-four degrees.