In the first place, therefore, we must define in how many modes the infinite may be said to subsist. According to one mode, then, that is called infinite which is not naturally adapted to be passed through; just as voice is said to be invisible. But, according to another mode, that is infinite the passage through which is without an end; or which has scarcely an end; or which though naturally adapted to be passed through or to have an end, yet has not. Again, everything which is infinite is so either by addition, or division, or according to both these modes. It is not possible, therefore, that the infinite, which is itself a certain infinite, should have a subsistence separate from sensibles: for if the infinite is neither magnitude nor multitude, but essence, and not accident, it will be indivisible: for that which is divisible will either be magnitude or multitude. But if it is indivisible, it will not be infinite, unless in the same manner as voice is invisible. Those, however, who say that there is the infinite, do not assert that it thus subsists, nor do we investigate it as a thing of this kind, but as that which cannot be passed through. But if the infinite subsists according to accident it will not be the element of beings, so far as it is infinite; as neither is the invisible the element of speech, although voice is invisible. Further still: how is it possible that anything should be the infinite itself? Since neither number nor magnitude can be so, of which the infinite is a certain essential passive quality: for it is still less necessary that there should be infinite, then that there should be number or magnitude. It is also evident that it is not possible for the infinite to be, as subsisting in energy, and as essence and a principle: for whatever part of it is assumed will be infinite, if it is partible: for the essence of infinite and the infinite are the same; since the infinite is essence or substance, and is not predicated of a subject. Hence it is either indivisible, or divisible into infinites. But it is impossible that there can be many infinites in the same thing. As air, however, is a part of air, so likewise infinite is a part of infinite, if it is essence and a principle. It is, therefore, impartible and indivisible. But this is impossible, since it is infinite in energy; for it is necessary that it should be a certain quantum. The infinite, therefore subsists according to accident. But if this be the case, it has been said that it cannot be called a principle; but this appellation must be given to that to which it is an accident, namely air, or the even number. So that they pronounce absurdly who thus speak, as the Pythagoreans assert: for at the same time they make the infinite to be essence, and distribute it into parts.
