The Life of Archytas

I. Archytas was a native of Tarentum, and the son of Mnesagoras; or, as Aristoxenus relates, of Histiæus.

I. Archytas was from Tarentum and was the son of Mnesagoras. According to Aristoxenus, however, his father was Histiæus.

II. He also was a Pythagorean; and he it was who saved Plato’s life by means of a letter, when he was in danger of being put to death by Dionysius.

II. He was also a Pythagorean. He saved Plato’s life with a letter when Dionysius was threatening to put Plato to death.

III. 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.

III. He was widely respected for his virtue in all things. His fellow citizens appointed him general seven times. No one else had ever held the office for more than one year, since the law forbade longer terms.

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

IV. Plato wrote letters to him because he had first written to Plato. His letter began as follows:

“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.”

“I am very glad that you have recovered from your poor health. You wrote to tell me so, and Lamiscus confirms it. I have been busy with some commentaries. I have also spent time among the Lucanians and met the descendants of Ocellus. I now have the treatises on Law, Kingly Power, Piety, and the Creation of the Universe, and I am sending them to you. I have not been able to find the rest, but I will send you any that I find.”

Thus wrote Archytas. And Plato sent him an answer in the following terms:—

This is what Archytas wrote. Plato replied as follows:

“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.”

“I was very glad to receive the Commentaries you sent me, and I greatly admire their author. He seems to us worthy of his ancient ancestors. They are said to have come originally from Myra and to have been among the Trojans Laomedon took with him. According to tradition, they were brave men. As for the Commentaries you asked me for, they are not yet finished, but I send them as they are. We both agree on the importance of taking care of such things, so I need not say more about that. Farewell.”

These then are the letters which these philosophers wrote to one another.

These are the letters the philosophers wrote to one another.

V. There were four people of the name of Archytas. The first, this man of whom we are speaking. The second was a Mytilenean, a musician. The third wrote a treatise on Agriculture. The fourth was an epigrammatic poet. Some writers also make mention of a fifth, who was an architect; and there is a book on mechanics extant which is attributed to him; which begins in this way:—

V. There were four people named Archytas. The first was the man we are discussing. The second was a musician from Mytilene. The third wrote a treatise on agriculture. The fourth was a poet who wrote epigrams. Some writers also mention a fifth Archytas, who was an architect. A surviving book on mechanics is attributed to him. It begins as follows:

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

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

And concerning the musician, the following story is told: That once he was reproached for not making himself heard, and he replied, “My organ contends on my behalf, and speaks.”

The following story is told about the musician. Once, someone criticized him for not making himself heard. He replied, “My instrument speaks and argues on my behalf.”

VI. Aristoxenus says, that this Pythagorean was never once 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.

VI. Aristoxenus says that this Pythagorean was never defeated as a general. But because others envied him, he once gave up his command, and his army was immediately taken prisoner.

VII. He was the first person who applied mathematical principles to mechanics, and reduced them to a system; and the first also who gave 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. He was also the first person who ever gave the geometrical measure of a cube, as Plato mentions in his Republic.

VII. He was the first to apply mathematical principles to mechanics and organize them into a system. He was also the first to give descriptive geometry a systematic direction. He did this by searching sections of a demicylinder for a mean proportional that would let him double a given cube. He was also the first to give the geometrical measure of a cube, as Plato mentions in his Republic.