second place is the dyad, a female number, and the same is called even by [Sidenote: p. 10.] the arithmeticians. In the third place is the triad, a male number, and it has been called odd by the arithmeticians’ decree. After all these is the tetrad, a female number, and this is also called even, because it is female. Therefore all the numbers derived from the genus[36] (now the illimitable genus is “number”) are four, from which was constructed, according to them, the perfect number, the decad. For the 1, 2, 3, 4 become 10 if for each number its appropriate name be substantially kept.[37] This decad Pythagoras said was a sacred Tetractys, a source of everlasting Nature containing roots within itself, and that from the same number all the numbers have their beginning. For the 11 and the 12 and the rest share the beginning of their being from the 10. The four divisions of the same decad, the perfect number, are called number, monad,[38] square[39] and cube. The conjunctions and minglings of [Sidenote: p. 11.] which make for the birth of increase and complete naturally the fruitful number. For when the square is multiplied[40] by itself, it becomes a square squared; when into the cube, the square cubed; when the cube is multiplied by the cube, it becomes a cube cubed. So that all the numbers from which comes the birth of things which are, are seven; to wit: number, monad, square, cube, square of square, cube of square and cube of cube. He declared also that the soul is immortal and that there is a change from one body to another.[41] Wherefore he said that he himself had been before Trojan times Aethalides,[42] and that in the Trojan era he was Euphorbus, and after that Hermotimus the Samian, after which Pyrrho of Delos, and fifthly Pythagoras. But Diodorus the Eretrian and Aristoxenus the writer on music[43] say that Pythagoras went to visit Zaratas[44] the Chaldæan; and Zaratas explained to him that there are from the beginning two causes of things that are, a father and mother: and that the father is light and the mother, darkness: and the divisions of the light are hot, dry, light (in weight) and swift; but those of the darkness cold, moist, heavy and slow. From these the [Sidenote: p. 12.] whole cosmos was constructed, to wit: from a female and a male; and that the nature of the cosmos[45] is according to musical harmony, wherefore the sun makes his journey rhythmically. And about the things which come into being from the earth and cosmos, they say Zaratas spoke thus: there are two demons,[46] a heavenly one and an earthly. Of these the earthly one sent on high a thing born from the earth which is water; but that the heavenly fire partook of the air, hot and cold. Wherefore, he says, none of these things destroys or pollutes the soul, for the same are the substance of all. And it is said that Pythagoras ordered that beans should not be eaten, because Zaratas said that at the beginning and formation of all things when