and nature, then, considering them pure, he enjoins them to speak. This man distributed his pupils into two orders, and called the one esoteric, but the other exoteric. And to the former he confided more advanced doctrines, and to the latter a more moderate amount of instruction.
And he also touched on magic—as they say—and himself[1] discovered an art of physiogony,[2] laying down as a basis certain numbers and measures, saying that they comprised the principle of arithmetical philosophy by composition after this manner. The first number became an originating principle, which is one, indefinable, incomprehensible, having in itself all numbers that, according to plurality, can go on ad infinitum. But the primary monad became a principle of numbers, according to substance,[3]—which is a male monad, begetting after the manner of a parent all the rest of the numbers. Secondly, the duad is a female number, and the same also is by arithmeticians termed even. Thirdly, the triad is a male number. This also has been classified by arithmeticians under the denomination uneven. And in addition to all these is the tetrad, a female number; and the same also is called even, because it is female. Therefore all the numbers that have been derived from the genus are four; but number is the indefinite genus, from which was constituted, according to them, the perfect[4] number, viz. the decade. For one, two, three, four, become ten, if its proper denomination be preserved essentially for each of the numbers. Pythagoras affirmed this to be a sacred quaternion, source of everlasting nature,[5] having, as it were, roots in itself; and that from this number all the numbers receive their originating principle. For eleven, and twelve, and the rest, partake of the origin of existence[6] from ten. Of this decade, the perfect number, there are termed four divisions,
