79. Archytas of Tarentum, son of Mnesagoras or, if we may believe Aristoxenus, of Hestiaeus, was another of the Pythagoreans. He it was whose letter saved Plato when he was about to be put to death by Dionysius. He was generally admired for his excellence in all fields; thus he was generalissimo of his city seven times, while the law excluded all others even from a second year of command. We have two letters written to him by Plato, he having first written to Plato in these terms:

“Archytas wishes Plato good health.

80. “You have done well to get rid of your ailment, as we learn both from your own message and through Lamiscus that you have: we attended to the matter of the memoirs and went up to Lucania where we found the true progeny of Ocellus [to wit, his writings]. We did get the works On Law, On Kingship, Of Piety, and On the Origin of the Universe, all of which we have sent on to you; but the rest are, at present, nowhere to be found; if they should turn up, you shall have them.”

This is Archytas's letter; and Plato's answer is as follows:

“Plato to Archytas greeting.

81. “I was overjoyed to get the memoirs which you sent, and I am very greatly pleased with the writer of them; he seems to be a right worthy descendant of his distant forbears. They came, so it is said, from Myra, and were among those who emigrated from Troy in Laomedon's time, really good men, as the traditional story shows. Those memoirs of mine about which you wrote are not yet in a fit state; but such as they are I have sent them on to you. We both agree about their custody, so I need not give any advice on that head. Farewell.”

These then are the letters which passed between them.

82. Four men have borne the name of Archytas: (1) our subject; (2) a musician, of Mytilene; (3) the compiler of a work On Agriculture; (4) a writer of epigrams. Some speak of a fifth, an architect, to whom is attributed a book On Mechanism which begins like this: “These things I learnt from Teucer of Carthage.” A tale is told of the musician that, when it was cast in his teeth that he could not be heard, he replied, “Well, my instrument shall speak for me and win the day.”

Aristoxenus says that our Pythagorean was never defeated during his whole generalship, though he once resigned it owing to badfeeling against him, whereupon the army at once fell into the hands of the enemy.

83. He was the first to bring mechanics to a system by applying mathematical principles; he also first employed mechanical motion in a geometrical construction, namely, when he tried, by means of a section of a half-cylinder, to find two mean proportionals in order to duplicate the cube.[78] In geometry, too, he was the first to discover the cube, as Plato says in the Republic.[79]

78↑ Cf. T. L. Heath, History of Greek Mathematics, i. 246-249.

79↑ 528 b.