But since every thing which is moved, is moved in time, and passes through a greater magnitude in a greater time; it is impossible that a finite space can be moved through in an infinite time, when that which is moved is neither always moved through the same, nor through some part of it, but is moved in the whole time through the whole. If, therefore, any thing is moved with an equal celerity, it is manifestly necessary that it should be moved through a finite magnitude in a finite time: for a part being assumed which will measure the whole space, in as many equal times as there arc parts, it is moved through the whole space. Hence, since these are finite, and each is a quantity, and all are assumed a certain number of times, the time also will be finite; for it will be so many times so much as the time of a part multiplied by the number of the parts. But if it should not be moved with an equal celerity, it is of no consequence: for let A and B be a finite interval, through which something is moved in an infinite time; and let the infinite time be C D. If, therefore, it is necessary that it should be moved through one part prior to being moved through another; this also is evident, that in the prior and posterior part of the time it will be moved through different parts of the interval; for in a further time it will always be moved through another part, whether it be changed with an equal or with an unequal celerity; and no less so, whether the motion suffers intention or remission, or whether it remains the same. Let, therefore, any part of the interval A B be assumed, viz. A E, which will measure the interval A B. This part, therefore, will be passed through in some portion of the infinite time; for it cannot be passed through in an infinite time, because the whole internal is passed through in an infinite time. Again, therefore, another part will necessarily be passed through in a finite time, if I assume a part as great as A E; since the whole is passed through in an infinite time. And thus by assuming one part after another, since there is no part of the infinite which measures it, (for it is impossible that the infinite should be composed from finites, whether they be equal or unequal; because things whiclt are finite in number and magnitude arc measured by a certain one; and that not the less whether they be equal or unequal, if they are of a definite magnitude,) and since the finite interval is measured by the quantity A E, — hence, that which is moved will be moved in a finite time through the space A B. The like also will take place in a progression to rest. So that neither is it possible for any thing to be generated or corrupted, which is always one and the same. The same reasoning also will prove that neither can any thing be moved through the infinite in a finite time, nor proceed to rest, whether it be equably or unequably moved: for any part being assumed which measures the whole time, in this part it will pass through a certain quantity, and not the whole of the magnitude; since it passes through the whole in the whole time. And again, in an equal part of the time it will pass through another quantity of the magnitude, and in a similar manner in each part of the time it will pass through some quantity of the magnitude, whether it be equal or unequal to the quantity which it passed through from the beginning; for it is of no consequence, if only each part be finite: for it is evident that the time being consumed, the infinite space will not be consumed, an ablation taking place which is finite, both with respect to quantity and number. So that it will not pass through an infinite magnitude in a finite time. Nor is it of any consequence, whether the magnitude is infinite on one side, or on both sides: for there will be the same reasoning. But these things having been demonstrated, it is evident that neither can a finite magnitude pass through an infinite space in a finite time, on account of the same cause: for in a part of the time it will pass through a finite space, and in a similar manner in the several parts: so that in the whole time it will pass through a finite space. But since a finite moveable does not pass through an infinite space in a finite time, it is evident that neither can an infinite moveable pass through a finite space; for if the infinite could pass through the finite, it is necessary that the finite also may pass through the infinite: for it is of no consequence which it is that is moved, since in both ways the finite will pass through the infinite: for when an infinite magnitude, as A, is moved, there will be some part of it in B finite, as, for instance, the part C D; and again, another and another part; and thus it will be perpetually. So that it will at the same time happen that the infinite will be moved through the finite, and the finite through the infinite: for it is not, perhaps, possible for the infinite to be moved through the finite in any other way than because the finite passes through the infinite, either by lation, or measuring it. So that, since this is impossible, the infinite cannot pass through the finite. But neither can an infinite magnitude pass through an infinite magnitude in a finite time: for if it can pass through the infinite, it can also pass through the finite, since the finitejs inherent in the infinite. Farther still, time also being assumed, there will be the same demonstration. But since neither a finite can pass through an infinite magnitude, nor an infinite a finite, nor through an infinite magnitude, in a finite time; it is evident that neither will there be an infinite motion in finite time; for what difference does it make, whether the motion or the magnitude is supposed to be infinite? For it is necessary, if either of these is infinite, that the other should be infinite also; because all lation is in place.
