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. CHAPTER XXXII. The division therefore into three, having been demonstrated by us, we shall briefly observe, that _the one_ appears to be many according to this order, _the one itself_ proceeding into a multitude of unities, and being in a similar manner becoming generated in conjunction with _the one_. For those three monads are the intelligible comprehensions of all orders, and they at once preside over all the progressions from intelligibles, produce all of them in an exempt manner, and collect them to the intelligible causes. Since however, Plotinus admits that number is prior to animal itself, and says that the first being produces from itself number, and that this is established as a medium between the one being, and animal itself, but is the basis and place of beings, it is worth while to speak likewise concisely about this. For if he says that animal itself has intelligible and occult number, as comprehended in the monad, he speaks rightly, and accords with Plato. But if he says that animal itself comprehends number, now separated, or which has a multiform subsistence, and is the progeny of difference, intelligible multitude is not a thing of this kind. For there indeed, _the one_ is being, and being is _the one_. Hence animal itself is according to all things perfect. But in number, _the one_ is separated from being, and being from _the one_, and each of the parts is no longer an intelligible whole, as an animal itself. For that is a whole of wholes; and every where _the one_ was with being in the parts of it, and animal itself was only-begotten. But number proceeded after the twofold coordinations, I mean the monad and duad, the odd and the even number. How therefore, can we place in animal itself the first number? If however, some one should say that number exists there, it is according to cause and intelligibly. But it is intellectually separated by difference. And farther still, in addition to these things, if animal itself is surveyed by some one in the demiurgic order, and he denominates it the plenitude of forms, and the intelligible of the demiurgic intellect, it will thus have intellectual number, as being arranged near the intellectual end.