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 an unmingled, and in another in a mingled manner. All things therefore, are here prolifically, but there, paternally and intelligibly. But that monad does not proceed from intelligibles, but subsists in them in unproceeding union. Hence, after these, and from these, we may survey the whole of number subsisting according to a third progression. “For these things,” says Parmenides, “preexisting, no number will be absent.”

Every number therefore, is generated through these in the third monad, and both the one and being become many, difference separating each of them. And every part indeed of being participates of the one; but every unity is carried as in a vehicle in a certain portion of being. Each of these however, is multiplied, intellectually separated, divided into minute parts, and proceeds to infinity. For as in intelligibles, we attribute infinite multitude to the third triad, so here, in this triad we assign infinite number to the third part of the triad. For in short every where, the infinite is the extremity, as proceeding in an all-perfect manner, and comprehending indeed all secondary natures, but being itself participated by none of them. In the first monad therefore, there were powers, but intelligibly. In the second, there were progressions and generations, but both intelligibly and intellectually. And in the third, there was all-powerful number, unfolding the whole of itself into light; and which also Parmenides denominates infinite. It is likewise especially manifest that it is not proper to transfer this infinity to quantity. For how can there be an infinite number, since infinity is hostile to the nature of number? And how are the parts of the one equal to the minute parts of being? For in infinites there is not the equal. But this indeed has been thought worthy of attention by those who were prior to us.