in seeking, in the sections of a demicylinder for a proportional mean, which should enable him to find the double of a given cube. He was also the first person who ever gave the geometrical measure of a cube, as Plato mentions in his Republic.
LIFE OF ALCMÆON.
I. Alcmæon was a citizen of Crotona; he also was a pupil of Pythagoras. And the chief part of his writings are on medical subjects; but he also at times discusses points of natural philosophy, and asserts that the greater part of human affairs have two sides. He appears to have been the first person who wrote a treatise on Natural Philosophy, as Phavorinus affirms, in his Universal History; and he used to argue that the moon had the same nature for ever which she had at that moment.
II. He was the son of Pirithus, as he himself states at the beginning of his treatise, where he says, “Alcmæon, of Crotona, the son of Pirithus, says