Archimedes

the members of the school had of attributing everything to the Master (αὐτὸς ἔφα, ipse dixit). In astronomy two things at least may safely be attributed to him; he held that the earth is spherical in shape, and he recognised that the sun, moon and planets have an independent motion of their own in a direction contrary to that of the daily rotation; he seems, however, to have adhered to the geocentric view of the universe, and it was his successors who evolved the theory that the earth does not remain at the centre but revolves, like the other planets and the sun and moon, about the “central fire”. Perhaps his most remarkable discovery was the dependence of the musical intervals on the lengths of vibrating strings, the proportion for the octave being 2 : 1, for the fifth 3 : 2 and for the fourth 4 : 3. In arithmetic he was the first to expound the theory of means and of proportion as applied to commensurable quantities. He laid the foundation of the theory of numbers by considering the properties of numbers as such, namely, prime numbers, odd and even numbers, etc. By means of figured numbers, square, oblong, triangular, etc. (represented by dots