ARCHYTAS, of Tarentum, son of Mnesagoras or Histi-aeus, was one of the most celebrated men of antiquity. He was. distinguished as a mathematician, a philosopher, a statesman, and a general; nor was he less remarkable for the purity and integrity of his life and the mildness and benevolence of his disposition. The time at which he flourished can be settled approximately from the fact that he was contemporary with Plato, whom he knew personally, and whose life he saved by interceding with the tyrant Dionysius. He took a prominent part in the administration of the state, and was seven times made general of the army, although by a law it was forbidden that any citizen should hold the command more than once. It is said that he was never defeated in battle. He was also intrusted with the charge of many important civil affairs. There seems to have been a tradition (see Horace, Odes, i. 28) that Archytas was drowned while crossing the Adriatic, but of this there is no certain information. Archytas belonged to the Pythagorean school of philosophy, and is said by some to have been the teacher of Philolaos. This, however, must certainly be an error. According to others, he was the eighth leader of the Pythagorean school. Fragments of writings, said to be his, on various points of ethical and metaphysical philosophy, are given by Stobaeus, Simplicius, and others. To portions of these Aristotle has been supposed to owe his doctrine of the Categories and s√me of his principal ethical theories. But it seems quite clear that scarcely any of these fragments are genuine, and that they belong to the 1st or 2d century A.D., a period during which Eclecticism, and a consequent desire to find traces of later doctrines in old writers, were the prevailing influences. Such fragments as do ...appear genuine are of no philosophical value, and are generally on special subjects. Archytas is particularly celebrated as a mathematician. To him are ascribed a solution of the problem of the duplication of the cube, and the application of analysis to the resolution of geometrical problems. He was also a skilled mechanician, and was one of the first to apply mathematics to mechanics and music. On the fragments of Archytas see Hartenstein, He Archy. Taren, frag., Leipsic, 1833; Gruppe, Ueber d. Frag. ,d. Archy., 1840; and Beckmann, De Pgthagor. Reliquiis ; also Zeller, Phil. d. Griech. 2d ed. iii. 2, 88, sqq,
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