employed mechanical motion in a geometrical construction, namely, when he tried, by means of a section of a half-cylinder, to find two mean proportionals in order to duplicate the cube. In geometry, too, he was the first to discover the cube, as Plato says in the Republic. 1* Chapter 5. ALCMAEON Alcmaeon of Croton, another disciple of Pythagoras, wrote chiefly on medicine, but now and again he touches on natural philosophy, as when he says, Most human affairs go in pairs." He is thought to have been the first to compile a physical treatise, so we learn from Favorinus in his Miscellaneous History ; and he said that the moon <and> generally <the heavenly bodies> are in their nature eternal. He was the son of Pirithous, as he himself tells us at the beginning of his treatise c : " These are the words of Alcmaeon of Croton, son of Pirithous, which he spake to Brotinus, Leon and Bathyllus : ' Of things invisible, as of mortal things, only the gods have certain knowledge ; but to us, as men, only inference from evidence is possible,' and so on." He held also that the soul is immortal and that it is continuously in motion like the sun. Chapter 6. HIPPASUS (fourth century b.c.) Hippasus of Metapontum was another Pythagorean, who held that there is a definite time which the