Herm. _I. G. P._ 16; _Dox._ 655. Others then from the ancient tribe, Pythagoras and his fellow-tribesmen, revered and taciturn, transmitted other dogmas to me as mysteries, and this is the great and unspeakable _ipse-dixit_: the monad is the first principle of all things. From its forms and from numbers the elements arose. And he declared that the number and form and measure of each of these is somehow as follows:—Fire is composed of twenty-four right-angled triangles, surrounded by four equilaterals. And each equilateral consists of six right-angled triangles, whence they compare it to the pyramid. Air is composed of forty-eight triangles, surrounded by eight equilaterals. And it is compared to the octahedron, which is surrounded by eight equilateral triangles, each of which is separated into six right-angled triangles so as to become forty-eight in all. And water is composed of one hundred and twenty triangles, surrounded by twenty equilaterals, and it is compared to the icosahedron, which is composed of one hundred and twenty equilateral triangles. And aether is composed of twelve equilateral pentagons, and is like a dodecahedron. And earth is composed of forty-eight triangles, and is surrounded by six equilateral pentagons, and it is like a cube. For the cube is surrounded by six tetragons, each of which is separated into eight triangles, so that they become in all forty-eight. X. _EMPEDOKLES._ Empedokles, son of Meton, grandson of an Empedokles who was a victor at Olympia, made his home at Akragas in Sicily. He was born about 494 B.C., and lived to the age of sixty. The only sure date in his life is his visit to Thourioi soon after its foundation (444). Various stories are told of his political activity, which may be genuine traditions; these illustrate a democratic tendency. At the same time he claimed almost the homage due to a god, and many miracles are attributed to him. His writings in some parts are said to imitate Orphic verses, and apparently his religious activity was in line with this sect. His death occurred away from Sicily—probably in the Peloponnesos. Literature:—Sturz, _Emped. vita et phil. carm. rell._ Lips. 1805; Karsten, _Emped. carm. rell._ Amst. 1838; Bergk, _Kleine Schriften_, Berl. 1839; Panzerbieter, _Beitr. z. Kritik u. Erkl. d. Emped._ Meining. 1844; Stein, _Emped. Frag._ Bonn 1852; Schneidewin, _Philol._ xv.; H. Diels; _Hermes_ xv. pp. 161-179; _Gorgias und Empedocles_, Acad. Berol. 1884; Unger, _Philol. Suppl._ 1883, pp. 511-550; O. Kern, _Archiv f. d. Gesch. d. Philos._ i. 498 ff.; Knatz, ‘Empedoclea’ in _Schedae Phil. H. Usener oblatae_, Bonn 1891; A. Platt, _Journal of Philology_, xxiv. p. 246; Bidez, _Archiv_, ix. 190; Gomperz, _Hermes_, xxxi. p. 469. NOTE.—I print Stein’s numbers at the left of the Greek text, Karsten’s numbers at the right. FRAGMENTS OF EMPEDOKLES. ΠΕΡΙ ΦΥΣΕΩΣ ΠΡΩΤΟΣ.