PHILOLAUS (b. c. 48o)  , Greek philosopher of the Pythagorean school, was born at Tarentum or at Crotona 1 (so Diog . Laert. viii . 84) . 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 . 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 (VeaviUKot), 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 distinctively 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 discovery of the regular solids is attributed to Pythagoras by Eudemus, and Empedocles is stated to have been the first who maintained that there are four 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, EK 6E TOU 6w6eKai6pov T7 v TOO sraVTOs o4 aipav and Stob . Eel . Phys. i . 10, 6 Tar v¢aipas 6XK6s) . This theory, however superficial from the standpoint of observation, indicates considerable knowledge of geometry and gave a great impulse to the study of the science . Following Parmenides, Philolaus 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 .

Eel . Phys . 488); but as these made up only nine revolving bodies he conceived, in accordance with his number theory, a tenth, which he called

counter-earth, aPr1xOwv . 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 365k days . He was the first who published a book on the Pythagorean doctrines, a treatise of which Plato made use in the composition of his Timaeus . This work of the Pythagorean, to which the mystical name Bauxat is sometimes given, seems to have consisted of three books: (r) Hepi K6o-uou, containing a general account of the origin and arrangement of the universe; (2) Hepi c/ioews, an exposition of the nature of numbers; (3) Hepi i'vxi3s, on the nature of the soul . Boeckh places his life between the loth and 95th Olympiads (496-396 inc.) . He was a contemporary of Socrates and Democritus, but senior to them, and was probably somewhat junior to Empedocles, so that his birth may be placed at about 480 . See Boeckh, Philolaus des Pythagoreers Lehren nebst den Bruchstiicken seines Werkes (Berlin, 1819) ; Schaarschmidt, Die angebliche Schriftstellerei des Philolaus (1864); also Fabricius, Bibliotheca graeca; Zeller, History of Greek Philosophy; Chaignet, Pythagore et la philosophic pythagorteienne, contenant les fragments de Philolaus et d`Architas (1873) ; Th . Gomperz, Greek Thinkers (Eng. trans . (1901), i .

123 sqq., 843 sqq. and authorities there quoted; also

art . PYTHAGORAS . For fragments see Ritter and Preller, Hist . Philosoph. ch. ii .