And that he used to forbid them to offer victims to the Gods, ordering them to worship only at those altars which were unstained with blood. He forbade them also to swear by the Gods; saying, “That every man ought so to exercise himself, as to be worthy of belief without an oath.” He also taught men that it behoved them to honour their elders, thinking that which was precedent in point of time more honourable; just as in the world, the rising of the sun was more so than the setting; in life, the beginning more so than the end; and in animals, production more so than destruction. Another of his rules was that men should honour the Gods above the dæmones, heroes above men; and of all men parents were entitled to the highest degree of reverence. Another, that people should associate with one another in such a way as not to make their friends enemies, but to render their enemies friends. Another was that they should think nothing exclusively their own. Another was to assist the law, and to make war upon lawlessness. Not to destroy or injure a cultivated tree, nor any animal either which does not injure men. That modesty and decorum consisted in never yielding to laughter, and yet not looking stern. He taught that men should avoid too much flesh, that they should in travelling let rest and exertion alternate; that they should exercise memory; that they should never say or do anything in anger; that they should not pay respect to every kind of divination; that they should use songs set to the lyre; and by hymns to the Gods and to eminent men, display a reasonable gratitude to them. He also forbade his disciples to eat beans, because, as they were flatulent, they greatly partook of animal properties [he also said that men kept their stomachs in better order by avoiding them]; and that such abstinence made the visions which appear in one’s sleep gentle and free from agitation. Alexander also says, in his Successions of Philosophers, that he found the following dogmas also set down in the Commentaries of Pythagoras:— That the monad was the beginning of everything. From the monad proceeds an indefinite duad, which is subordinate to the monad as to its cause. That from the monad and the indefinite duad proceed numbers. And from numbers signs. And from these last, lines of which plane figures consist. And from plane figures are derived solid bodies. And from solid bodies sensible bodies, of which last there are four elements; fire, water, earth, and air. And that the world, which is endued with life, and intellect, and which is of a spherical figure, having the earth, which is also spherical, and inhabited all over in its centre, results from a combination of these elements, and derives its motion from them; and also that there are antipodes,[112] and that what is below, as respects us, is above in respect of them.