Lives and Opinions of Eminent Philosophers

​Archytas of Tarentum was the son of Mnesagoras, or according to Aristoxenus, of Hestiaeus; he too was a Pythagorean. It was he who rescued Plato by letter from Dionysius when he was about to be put to death. He was also admired by the multitude for every excellence; indeed, he served as general of the citizens seven times, whereas the others did not serve for more than a single year because the law forbade it. Plato also wrote two letters to him, since he had previously written to Plato in the following manner: “Archytas to Plato, greetings.

“You do well in having recovered from your illness; for you yourself sent word of this, and the companions of Lamiscus also reported it. As for the treatises, we looked after them and went up to the Lucanians, where we met with the descendants of Ocellus. The treatises *On Law*, *On Kingship*, *On Piety*, and *On the Origin of the Universe* we possess ourselves and have dispatched to you; but the remainder cannot be found at present, though if it is found, it will come to you.” Thus wrote Archytas; and Plato sent this reply in turn: “Plato to Archytas, greetings.

“The treatises that came from you we received with astonishing pleasure, and we admired their author in the highest degree; and he seemed to us a man worthy of those ancient ancestors. For indeed these men are said to be Myraioi; and they were noble men among the Trojans who emigrated under Laomedon, as the handed-down myth shows. The treatises from me about which you wrote are not yet in adequate shape; but just as they happen to be, I have dispatched them to you. As for their safekeeping, we are both in agreement, so that there is no need of any urging. Farewell.” And such are the letters they exchanged with each other.

​There have been four men named Archytas: the first is this very man; the second, a musician from Mytilene; the third, the author of a work *On Agriculture*; the fourth, an epigrammatist. Some also speak of a fifth, an architect, under whose name a book *On Mechanics* is circulated, having this opening: “These things I learned by inquiry from Teucer the Carthaginian.” Concerning the musician, this is also reported: that, when reproached for not being heard clearly, he said: “For the instrument speaks, competing on my behalf.” Aristoxenus says that the Pythagorean Archytas was never defeated while serving as general; but once, being envied, he stepped down from his generalship, and his men were immediately captured.

​He was the first to systematize mechanics by applying mathematical principles to them, and the first to introduce mechanical motion into a geometric diagram, seeking to find two mean proportionals through the section of a semi-cylinder for the duplication of the cube. He was also the first in geometry to discover the cube, as Plato says in the *Republic*.