It remains then, that we should speak concerning the triadic division of it, following Parmenides. These three things therefore, have appeared to us from the beginning, according to the separation of the one from being, viz. the one, difference, and being; difference not being the same either with the one or being. For though the one and being were in intelligibles, yet difference first subsists here. Since however power above [i.e. in intelligibles] was collective, but here is the separator of the extremes, there are not only three monads, but also three duads, viz. the one in conjunction with difference, difference in conjunction with being, and the one in conjunction with being. For difference also is the cause of a separation of this kind, not preserving the union of the one being with genuine purity. There are therefore three monads, and three duads. But these likewise may become three triads, when we begin, at one time from the one, at another time from being, and at another from difference. Hence this triad subsists monadically, and triadically. But this is the same thing as to assert that difference and the first feminine nature generates in itself, monads, duads, and triads. For the divided assumption, generates for us different monads; but the conjoined assumption, duads, and triads, some indeed being vanquished by the one, others by difference, and others by being. And thus far the first deity presents itself to the view, being prolific of the first numbers; according to the one indeed, of unical numbers, but according to difference of generative, and according to being, of essential numbers.

Since however, from this deity which is intelligible, that which is posterior to it proceeds, it is evidently necessary that the monad, duad, and triad, should severally have prolific power. These powers therefore, Parmenides calls once, twice, thrice. For each of these is a power which is the cause of the above-mentioned essences that produce either separately, or connectedly. For there with respect to the generations of them, some of them are entirely peculiar, but others are common to secondary natures. The progeny therefore of these are, the oddly-odd, the evenly-even and the evenly-odd.[243] And of these, the oddly-odd indeed, as we have before observed, is collective into union of the divine progressions. But the evenly-even is generative of wholes, and proceeds as far as to the last of things. The evenly-odd however, is mixed, having its subsistence from both the even and the odd. Hence we must establish the first as analogous to bound, but the second as analogous to power, and the third as analogous to being. And you may see, how indeed in the first order all things had a primary subsistence, viz. monad, duad, triad; but how in this order, all things are secondarily and subordinately. And the mixture which is the triad, subsisted there indeed in one way, but here the evenly-odd subsists in another way. For there the extremes were odd, because they were intelligible; but here the even is more abundant, and the intelligible summit only is odd. For the middle of the triad is analogous to power. And there indeed, is the monad, which has all the forms of odd numbers according to cause, and the duad is there, which is occultly all the forms of even numbers, and also the triad, which is number primarily. But here both the odd and the even number now subsist in a twofold respect, in one place in 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.