Archytas: Pythagoreans

¹ Archytas was:

• a native of Tarentum
• the son of Mnesagoras; or, as Aristoxenus relates, of Histiæus.

² He also was a Pythagorean

He saved Plato’s life through a letter, when he was in danger of being put to death by Dionysius.

³ He was a man held in very general esteem on account of his universal virtue; and he was seven times appointed general of his countrymen, when no one else had ever held the office for more than one year, as the law forbade it to be held for a longer period.

⁴ Plato wrote his letters to him; as he had begun the correspondence by writing himself to Plato, which he did in the following manner:—

ARCHYTAS TO PLATO, GREETING.

“I am very glad that you have recovered from your delicate state of health; for you yourself have sent me word of your recovery, and Lamiscus gives the same account. I have been much occupied with some commentaries, and have been among the Lucanians, and have met with the descendants of Ocellus. I have now in my possession, and I send to you the treatises on Law, and Kingly Power, and Piety, and the Creation of the Universe. As for the rest, I have not been able to find them, but whenever I do find any, I will send them to you.”

Plato sent him a reply:

PLATO TO ARCHYTAS, GREETING.

“I was exceedingly glad to receive the Commentaries which came from you, and I have admired their author in the greatest possible degree; and he seems to us to be a man worthy of his ancient ancestors. For they are said to have been originally natives of Myra; and to have been among the Trojans, whom Laomedon took with him, gallant men, as the story handed down by tradition attests. As for my Commentaries which you ask me for, they are not yet completed, but such as they are I send them to you. And on the propriety of taking care of such things we are both agreed, so that I have no need to impress anything on you on that head. Farewell.”

⁵ There were 4 other people named Archytas.

1. a musician Mytilenean

Once he was reproached for not making himself heard, and he replied, “My organ contends on my behalf, and speaks.”

2. the writer of a treatise on Agriculture
3. an epigrammatic poet
4. an architect who wrote a book on mechanics which begins in this way:

“This is what I heard from Teucer, the Carthaginian.”

⁶ Aristoxenus says that this Pythagorean was never defeated while acting as general.

But that as he was attacked by envy, he once gave up his command, and his army was immediately taken prisoner.

⁷ He was the first to:

• apply mathematical principles to mechanics, and reduced them to a system.
• give a methodical impulse to descriptive geometry in seeking, in the sections of a demicylinder for a proportional mean, which should enable him to find the double of a given cube.
• give the geometrical measure of a cube, as Plato mentions in his Republic.