VIII. He was the first person, as Timæus says, who asserted that the property of friends is common, and that friendship is equality. And his disciples used to put all their possessions together into one store, and use them in common; and for five years they kept silence, doing nothing but listen to discourses, and never once seeing Pythagoras, until they were approved; after that time they were admitted into his house, and allowed to see him. They also abstained from the use of cypress coffins, because the sceptre of Jupiter was made of that wood, as Hermippus tells us in the second book of his account of Pythagoras. IX. He is said to have been a man of the most dignified appearance, and his disciples adopted an opinion respecting him, that he was Apollo who had come from the Hyperboreans; and it is said, that once when he was stripped naked, he was seen to have a golden thigh. And there were many people who affirmed, that when he was crossing the river Nessus it addressed him by his name. X. Timæus, in the tenth book of his Histories, tells us, that he used to say that women who were married to men had the names of the Gods, being successively called virgins, then nymphs, and subsequently mothers. XI. It was Pythagoras also who carried geometry to perfection, after Mœris had first found out the principles of the elements of that science, as Aristiclides tells us in the second book of his History of Alexander; and the part of the science to which Pythagoras applied himself above all others was arithmetic. He also discovered the numerical relation of sounds on a single string: he also studied medicine. And Apollodorus, the logician, records of him, that he sacrificed a hecatomb, when he had discovered that the square of the hypothenuse of a right-angled triangle is equal to the squares of the sides containing the right angle. And there is an epigram which is couched in the following terms:— When the great Samian sage his noble problem found, A hundred oxen dyed with their life-blood the ground.