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.
Alcmaeon was a citizen of Crotona; he also was a pupil of Pythagoras. And the chief part of his writings are on medical subjects; but he also at times discusses points of natural philosophy, and asserts that the greater part of human affairs have two sides. He appears to have been the first person who wrote a treatise on Natural Philosophy, as Phavorinus affirms, in his Universal History; and he used to argue that the moon had the same nature forever which she had at that moment.
He was the son of Pirithus, as he himself states at the beginning of his treatise, where he says, “Alcmaeon of Crotona, the son of Pirithus, says this to Brontinus, and Leon, and Bathyllus. About things invisible, and things mortal, the Gods alone have a certain knowledge; but men may form conjectures. …” And so on.
He used also to say that the soul was immortal, and that it was in a state of perpetual motion in the same way as the sun.
Hippasus was a citizen of Metapontum, and a pupil of Pythagoras.
He used to say that the time of the changes of the world was definite, and that the universe also was finite, and in a state of perpetual motion.
Demetrius, in his treatise on People of the Same Name, says that he left no writings behind him.
There were two people of the name of Hippasus: this man, and another who wrote an account of the Constitution of the Lacedaemonians in five books. And he was himself a Lacedaemonian.
Philolaus was a native of Crotona, and a pupil of Pythagoras; it was from him that Plato wrote to Dion to take care and purchase the books of Pythagoras.
And he died under suspicion of having designed to seize on the tyranny; and we have written an epigram on him:
I say that all men ought above all things To guard against suspicion. For, though innocent, Still if you are suspected, you’re unfortunate. And thus his native city of Crotona Slew Philolaus; for the jealous citizens Thought that his house betrayed a tyrant’s purpose.
His theory was that everything was produced by harmony and necessity. And he was the first person who affirmed that the earth moved in a circle; though some attribute the assertion of this principle to Icetas of Syracuse.
He wrote one book, which Hermippus reports, on the authority of some unknown writer, that Plato the philosopher purchased when he was in Sicily (having come thither to the court of Dionysius), of the relations of Philolaus, for forty Alexandrian minae of silver; and that from this book he copied his Timaeus. But others say that Plato received it as a present, after having obtained his liberty for a young man, one of the disciples of Philolaus, who had been arrested by Dionysius. Demetrius, in his treatise on people of the same name, says that he was the first of the Pythagoreans who wrote a treatise on Natural Philosophy; and it begins thus:
But nature in the world has been composed of bodies infinite and finite, and so is the whole world and all that is in it.
Eudoxus was the son of Aeschines, and a native of Cnidus. He was an astronomer, a geometrician, a physician, and a lawgiver. In geometry he was a pupil of Archytas, and in medicine of Philistion the Sicilian, as Callimachus relates in his Tablets; and Sotion, in his Successions, asserts that he was likewise a pupil of Plato; for that, when he was twenty-three years of age, and in very narrow circumstances, he came to Athens with Theomedon the physician, by whom he was chiefly supported, being attracted by the reputation of the Socratic school. Some say that his attachment to Theomedon was cemented by nearer ties. And when he had arrived at Piraeus, he went up to the city every day, and when he had heard the Sophists lecture he returned. And having spent two months there, he returned home again; and being again aided by the contributions of his friends, he set sail for Egypt, with Chrysippus the physician, bearing letters of introduction from Agesilaus to Nectanabis, and that he recommended him to the priests.
And having remained there a year and four months, he shaved his eyebrows after the manner of the Egyptian priests, and composed, as it is said, the treatise called the Octaeteris. From thence he went to Cyzicus, and to the Propontis, in both of which places he lived as a Sophist; he also went to the court of Mausolus. And then, in this manner, he returned again to Athens, having a great many disciples with him, for the sake, as some say, of annoying Plato, because he had originally discarded him from his school. Some say that when Plato gave an entertainment on one occasion, Eudoxus, as the guests were very numerous, introduced the fashion of sitting in a semicircle.
Nicomachus, the son of Aristotle, affirms that he used to say that pleasure was the good.
He was received in his own country with great honors, as the decree that was passed respecting him shows. He was also accounted very illustrious among the Greeks, having given laws to his own fellow citizens, as Hermippus tells us in the fourth book of his account of the Seven Wise Men; and having also written treatises on Astronomy and Geometry, and several other considerable works.
He had three daughters: Actis, Philtis, and Delphis. And Eratosthenes asserts, in his books addressed to Baton, that he also composed dialogues entitled Dialogues of Dogs; others say that these were written by some Egyptians, in their own language, and that Eudoxus translated them and published them in Greece. One of his pupils was Chrysippus of Cnidos, son of Erineus, who learnt of him all that he knew about the Gods, and the world, and the heavenly bodies; and who learnt medicine from Philistion the Sicilian. He also left some very admirable Reminiscences.
He had a son of the name of Aristagoras, who was the teacher of Chrysippus, the son of Aëthlius; he was the author of a work on Remedies for the Eyes, as speculations on natural philosophy had come very much under his notice.
There were three people of the name of Eudoxus: The first, this man of whom we are speaking; the second, a Rhodian, who wrote histories; the third, a Siciliot, a son of Agathocles, a comic poet, who gained three victories at the Dionysia in the city, and five at the Lenaea, as Apollodorus tells us in his Chronicles. We also find another, who was a physician of Cnidos, who is mentioned by this Eudoxus, in his Circuit of the World, where he says that he used to warn people to keep constantly exercising their limbs in every kind of exercise, and their senses too.
The same author says that the Cnidean Eudoxus flourished about the hundred and third olympiad; and that he was the inventor of the theory of crooked lines. And he died in his fifty-third year. But when he was in Egypt with Conuphis of Heliopolis, Apis licked his garment; and so the priests said that he would be short-lived, but very illustrious, as it is reported by Phavorinus in his Commentaries. And we have written an epigram on him, that runs thus:
’Tis said, that while at Memphis wise Eudoxus Learnt his own fate from th’ holy fair-horned bull; He said indeed no word, bulls do not speak Nor had kind nature e’er calf Apis gifted With an articulately speaking mouth. But standing on one side he lick’d his cloak, Showing by this most plainly—in brief time You shall put off your life. So death came soon, When he had just seen three and fifty times The Pleiads rise to warn the mariners.
And instead of Eudoxus, they used to call him Endoxus, on account of the brilliancy of his reputation. And since we have gone through the illustrious Pythagoreans, we must now speak of the Promiscuous philosophers, as they call them. And we will first of all speak of Heraclitus.