Aet. _Plac._ i. 3; _Dox._ 280. And again from another starting-point, Pythagoras, son of Mnesarchos, a Samian, who was the first to call this matter by the name of philosophy, assumed as first principles the numbers and the symmetries existing in them, which he calls harmonies, and the elements compounded of both, that are called geometrical. And again he includes the monad and the undefined dyad among the first principles; and for him one of the first principles tends toward the creative and form-giving cause, which is intelligence, that is god, and the other tends toward the passive and material cause, which is the visible universe. And he says that the starting-point of number is the decad; for all Greeks and all barbarians count as far as ten, and when they get as far as this they return to the monad. And again, he says, the power of the ten is in the four and the tetrad. And the reason is this: if any one †returning† from the monad adds the numbers in a series as far as the four, he will fill out the number ten (_i.e._ 1 + 2 + 3 + 4 = 10); but if he goes beyond the number of the tetrad, he will exceed the ten. Just as if one should add one and two and should add to these three and four, he will fill out the number ten; so that according to the monad number is in the ten, but potentially in the four. Wherefore the Pythagoreans were wont to speak as though the greatest oath were the tetrad: ‘By him that transmitted to our soul the tetraktys, which has the spring and root of ever-flowing nature.’ And our soul, he says, is composed of the tetrad; for it is intelligence, understanding, opinion, sense, from which things come every art and science, and we ourselves become reasoning beings. The monad, however, is intelligence, for intelligence sees according to the monad. As for example, men are made up of many parts, and part by part they are devoid of sense and comprehension and experience, yet we perceive that man as one alone, whom no being resembles, possesses these qualities; and we perceive that a horse is one, but part by part it is without experience. For these are all forms and classes according to monads. Wherefore, assigning this limit with reference to each one of these, they speak of a reasoning being and a neighing being. On this account then the monad is intelligence by which we perceive these things. And the undefined dyad is science; fittingly, for all proof and all persuasion is part of science, and farther every syllogism brings together what is questioned out of some things that are agreed upon, and easily proves something else; and science is the comprehension of these things, wherefore it would be the dyad. And opinion as the result of comprehending them is the triad; fittingly, for opinion has to do with many things; and the triad is quantity, as ‘The thrice-blessed Danaoi.’ On this account then he includes the triad.... And their sect is called Italic because Pythagoras taught in Italy, for he removed from Samos, his