the Argive Possiden (both of them being Pythagoreans), went to him, and not manifesting what he intended to do, advised him to return to his native country, with all possible celerity, and having placed him in a ship that was then sailing near the shore, supplied him with what was necessary for his voyage, and thus saved the man from the dangers [to which he was exposed]. In short, he who should relate all that has taken place among the Pythagoreans in their associations with each other, would by the length of his narration exceed the proper quantity and the occasion of his treatise. I shall therefore rather pass on to show, that some of the Pythagoreans were political characters, and adapted to govern. For they were guardians of the laws, and ruled over certain Italian cities, unfolding to them, and counselling them to adopt the most excellent measures, but abstaining from public revenues. And though they were greatly calumniated, yet at the same time the probity of the Pythagoreans, and the wish of the cities themselves prevailed, so that they were desired by them to administer their political concerns. But at this time the most beautiful of polities appear to have existed in Italy and in Sicily. For Charondas the Catanean, who appears to have been one of the best legislators, was a Pythagorean; as were also the Locrians Zaleucus and Timares, who were celebrated for their legislation. Those also who established the Rheginic polities, that polity which is called Gymnasiarchic, and that which is denominated from Theocles, are said to have been Pythagoreans. Phytius likewise, Theocles, Elecaon, and Aristocrates, excelled among the Pythagoreans in their studies and manners, which also the cities in those places adopted at those times. In short, it is asserted that Pythagoras was the inventor of the whole of political erudition, when he said that nothing is pure among things that have an existence; but that earth participates of fire, fire of air, air of water, and water of spirit. And in a similar manner the beautiful participates of the deformed, the just of the unjust, and other things conformably to these. From this hypothesis, however, the reasoning tends to either part. He also said, that there are two motions of the body and the soul; the one being irrational, but the other the effect of deliberate choice. That three certain lines also constitute polities, the extremes of which mutually touch each other, and produce one right angle; so that one of them has the nature of the sesquitertian; another that of the diapente; and the third is a medium between the other two.[33] But when we consider by a reasoning process the coincidences of the lines with each other, and also of the places under these, we shall find that they represent the best image of a polity. Plato has made the glory of this invention his own; for he clearly says in his Republic, “that the sesquitertian progeny conjoined