That many absurdities, however, will happen if the infinite has not any subsistence whatever, is evident; for of time there will be some beginning and end; magnitudes also will not be divisible into magnitude; and number will not be infinite. But this being determined, since it does not appear that either of these consequences can be admitted, on this account it is evident that the infinite, in one respect, is, and then another respect is not. But one thing is said to have a subsistence in capacity, and another in energy. And the infinite partly subsists by addition, and partly by ablation. With respect to magnitude, however, that it is not infinite in energy, we have already said, but it is infinite by division: for it is not difficult to subvert the hypothesis of indivisible lines. It remains, therefore, that the infinite is in capacity. That, however, which is infinite in capacity, is not to be assumed as that which will be infinite in energy, in the same manner as if this thing has the capacity of becoming a statue, it will be a statue. But since being is predicated in many ways, as a day is, and a contest is, because another and another is always becoming to be, so also is the infinite: for in these there is both capacity and energy: for the Olympic Games are, both because a contest may be effected, and because it is becoming to be. But the infinite is manifest differently in time, in men, and in the division of magnitudes: for, in short, the infinite thus subsists, because another and another part may always be assumed; and that which is assumed is always finite, but there is always another and another part. So that the infinite must not be considered as this particular thing, as, for instance, a man or a house, but as a day and a contest are said to subsist, (the being of which is not generated, as a certain essence, but always consists in generation or corruption) which though they are finite, yet there is always another and another. This, however, happens in magnitudes that remaining which was assumed; but in men and time, these being corrupted so as not to fail. But the infinite according to addition, is in a certain respect the same as that according to division: for in that which is finite according to addition, it takes place conversely; since so far as it is seen to be divisible to infinity, so far it appears to be added to that which is infinite: for in a finite magnitude, if anyone assuming a definite part, again assumes it in the same ratio, not taking the same part of the whole in that ratio, he will not arrive at the end of the finite magnitude. But if he so increases the ratio, as always to assume the same magnitude, he will arrive at the end, because every finite quantity is consumed by any finite quantity. The infinite, therefore, does not subsist in any other way than this: for it has its being in capacity, and in division and diminution. It is also in energy, in the same manner as we say a day and a contest are. It is likewise in capacity, in the same manner as matter: and it does not subsist per se, like that which is finite. Hence it is thus infinite in capacity according to addition; because we say it is after a certain manner the same as the infinite according to division: for it is always possible to assume something beyond it. It does not, however, on this account surpass every definite magnitude; as in division it surpasses every definite magnitude, and will be less. So that it is not possible for the infinite to surpass every magnitude by addition, even in capacity, unless the infinite should be in energy from accident, according to the assertion of those physiologists who introduce an infinite body beyond the world, the essence of which is air, or some other infinite of this kind. But if it is not possible that an infinite sensible body can thus subsist in energy, it is evident that neither can the infinite, according to addition, subsist in capacity, unless as we have said, in a manner, vice versato division: for Plato, also, on this account introduces two infinites, because both in increase and diminution there appears to be transcendency, and a progression to infinity. Though, however, he introduced two, he did not use them: for neither is there infinity in numbers by diminution or division; since unity is a minimum: nor by increase; for he extends number as far as to the decad.
