PHILOLAUS (b. c. 480), Greek philosopher of the Pytha gorean school, born at Tarentum or at Crotona (so Diog. Laert. viii. 84), was probably a teacher of Democritus. After the death of Pythagoras great dissensions prevailed in the cities of lower Italy. According to some accounts, Philolaus, obliged to flee, took refuge first in Lucania and then at Thebes, where he had as pupils Simmias and Cebes, who subsequently, being still young men, were present at the death of Socrates. Before this Philolaus had returned to Italy, where he was the teacher of Archytas. He entered deeply into the Pythagorean number theory, particularly dwelling on the properties inherent in the decad--the sum of the first four numbers, consequently the fourth triangular number, the tetractys (see Vit. Pythag. ap. Phot. Bibl. p. 712)— which he called great, all-powerful, and all-producing. The great Pythagorean oath was taken by the sacred tetractys. The dis covery of the regular solids is attributed to Pythagoras by Eude mus, and Empedocles is stated to have been the first who main tained that there are f our elements. Philolaus, connecting these ideas, held that the elementary nature of bodies depends on their form, and assigned the tetrahedron to fire, the octahedron to air, the icosahedron to water, and the cube to earth; the dodecahedron he assigned to a fifth element, aether, or, as some think, to the universe (see Plut. de Pl. Ph. ii. 6, iK bi 7-01) bcobeicagpov rip roi) rapTos and Stob. Ecl. Phys. i. io, o ras acktipas 6XKOs). This theory, however superficial from the standpoint of observation, indicates considerable knowledge of geometry and gave a great impulse to its study. Following Parmenides, Philo- ' laus regarded the soul as a "mixture and harmony" of the bodily parts; he also assumed a substantial soul, whose existence in the body is an exile on account of sin.
Philolaus was the first to propound the doctrine of the motion of the earth; some attribute this doctrine to Pythagoras, but there is no evidence in support of their view. Philolaus supposed that the sphere of the fixed stars, the five planets, the sun, moon and earth, all moved round the central fire, which he called the hearth of the universe, the house of Zeus, and the mother of the gods (see Stob. Ecl. Phys. i. 488) ; but as these made up only nine revolving bodies he conceived, in accordance with his num ber theory, a tenth, which he called counter-earth, avrtxOcWv. He supposed the sun to be a disk of glass which reflects the light of the universe. He made the lunar month consist of 291 days, the lunar year of 354, and the solar year of 365-1 days. He was the first who published a book on the Pythagorean doctrines, a trea tise used by Plato in the composition of his Timaeus and to which the mystical name B6Kxat is sometimes given.