PHILOLAUS, next to Archytas the most illustrious of the Pythagorean philosophers, was born at Tarentum or, according to Diogenes Laertius, at Crotona. He was said to have been intimate with Democritus, and was probably one of his teachers. After the death of Pythagoras great dissensions prevailed in the cities of lower Italy, which were allayed only after the lapse of many years through the intervention of the Achaeans. According to some accounts Philolaus was obliged to flee, and owed his escape to his youthful energy. He took refuge first in Lucania, then in Greece; he lived at Thebes, where he had for pupils Simmias and Cebes, who subsequently, being still young men {νεανίσκοι), were present at the death of Socrates. Prior to this Philolaus had left Thebes and returned to Italy, where he was the teacher of Archytas. Pythagoras published nothing, nor did the other early Pythagoreans; the members of the brotherhood, moreover, piously referred their discoveries back to their master; hence many doctrines have been attributed to Pythagoras which were first propounded later in the school. He entered deeply into the number-theory, which constituted the distinctive feature of the Pythagorean philosophy, and in particular dwelt on the properties inherent in the decad —the sum of the first four numbers, consequently the fourth triangular number, the tetractys—which he called great, all-powerful, and all-producing. The discovery of the regular solids is attributed to Pythagoras by Eudemus, and Empedocles is stated to have been the first who maintained that there were four elements. Philolaus, connecting these ideas, held that the elementary nature of bodies depended on their form, and assigned the tetrahedron to fire, the octahedron to air, the icosahedron to ...