Again, however, we shall say, that there is not a vacuum so separate as some assert it to be: for if there is a certain natural lation to each of the simple bodies, as for instance, to fire upward, but to earth downward, and toward the middle, it is evident that a vacuum will not be the cause of lation. Of what then will a vacuum be the cause? For it appears to be the cause of motion according to place; and yet is not the cause of this. Further still; if it is any thing, as for instance a place deprived of body, whither will the body placed in it be impelled? For it will not be impelled in all directions. The same reasoning also may be urged against those who fancy that place is something separate into which that is carried which is borne along: for how will that which is in this be either impelled or abide? And the same reasoning will fitly accord to upward and downward, and to a vacuum: for those who say there is a vacuum make it to be place. How therefore will body be in place, or in a vacuum? For this cannot happen, since the whole of some body is considered as being in a separate and permanent place: for a part of such a body, unless it is considered separately, will not be in place, but in the whole.
Again, if place is not separate from body, neither will a vacuum. But to him who considers this affair, it will appear that the contrary rather happens to those who say there is a vacuum, as if this were necessary if there is motion; I mean that nothing can be moved if there is a vacuum: for just as those who say that the earth is at rest through similitude; so likewise it is necessary to be at rest in a vacuum: for there is not any place in it where a thing can be more or less moved: since so far as it is a vacuum it has not any difference. In the first place, therefore, because every motion is either from violence, or according to nature, it is necessary, if there is violent that there should also be natural motion: for violent motion is contrary to nature; and that which is contrary to nature is posterior to that which is according to nature. So that if motion according to nature is not present with every natural body, neither will any one of the other motions be present. Besides, how will it be natural, since there is no difference in a vacuum and the infinite? For so far as it is infinite there will be no downward, nor upward, nor middle; but so far as it is a vacuum, there will be no difference between the downward and upward: for as there is no difference in nothing, so neither is there in non-entity. But a vacuum appears to be a certain non-entity and privation. Natural lation however is different; so that things which are naturally moved will be different. Either, therefore, there will not be any where a natural lation to any thing, or if there is, there is not a vacuum. Further still; things which are thrown are now moved, he who impels them not touching them, either through an antiperistasis, as some say; or because the air being impelled, impels with a swifter motion than that of the lation of the impelled body through which it tends to its proper place. But in a vacuum there can be nothing of this kind ; nor can any thing be borne along, unless as that which is carried. Again, no one can assign a reason why that which is in motion stops somewhere: for why should it rather stop bere than there? So that either it will be at rest, or it is necessary that it should be borne along to infinity, unless some thing more powerful impedes. Further still; now it seems to be carried to a vacuum, because it yields; but in a vacuum a thing of this kind is similarly every way; so that it will be every way impelled. Again, what is said will be evident from the following considerations. We see the same weight and body more swiftly borne along, through two causes; either because there is a difference in that th.rough which it is borne along, as when it moves through water, or earth, or air; or because that which is borne along differs, if other things remain the same, through excess of weight, or levity. Hence that through which it is borne along is the cause that it impedes, especially if it is borne in a contrary direction, and in the next place if it abides. But this is more especially the case with that which is not easily divided; and that which is more dense is a thing of this kind. Let the weight A, therefore, be impelled through B in the time G; but through D, which is more attenuated in the time E, if the length of B is equal to that of D, according to the proportion of the impeding body: for let B be water, but D air. By how much the more attenuated, therefore, and incorporeal, air is then water, by so much swifter will A be impelled through D than through B. It will therefore have the same ratio of celerity to celerity, as air to water. So that if it is doubly more attenuatcd, it will pass through the space B in double the time that it will pass through D; and the time G will be double the time E. And thus always by how much the more incorporeal that is through which it passes, and by how much less it impedes, and may be more easily divided, by so much the more swiftly will it be impelled. But a vacuum has no ratio by which it may be surpassed by body; just as nothing has no ratio to number; for if four surpasses three by one, but two by more than one, and one by still more than it surpasses two,· there will no longer be any ratio by which it surpasses nothing: for it is necessary that what surpasses should be divided into excess, and that which is exceeded; so that four will be divided into four, and nothing. Hence, neither can a line surpass a point, unless it were composed from points. In like manner, neither can a vacuum have any ratio to a plenum; and therefore neither the motion through the one to the motion through the other. But if a weight passes through so much space in such time, through a most attenuated medium; in passing through a vacuum it will exceed every ratio: for let Z be a vacuum, equal to the magnitudes Band D. If, therefore, it passes through A, and is moved in a certain time, viz. in the time E, which is less than the time F, the vacuum also will have this ratio to the plenum. But in as much time as E the weight A will pass through G a part of D. But it will also pass through it, even if there should be something in Z differing in subtility from air, in the same proportion as the time E to the time F; for if the body in Z is as much more attenuated than D as the time E surpasses the time F; vice versa, the weight A, if it is borne along, will pass through Z with a celerity measured by the time, F. F. If, therefore, there is no body in Z, it will pass through it with still greater celerity: but it was in the time F. So that in an equal time it wilt pass through a plenum and a vacuum. This, however, is impossible. It is evident, therefore, that if there should be any time in whicll any thing whatever is impelled through a vacuum, this impossibility would happen : for let it be assumed that any thing will pass through a plenum and a vacuum in an ·equal time: then there will be some body having the same ratio to another as time to time. And to sum up the whole in a few words, the cause of that which happens is manifest; viz. that there is a ratio of every motion to every motion: for it is in time; but there is a ratio of every time to every time, both being finite. But there is no ratio of a vacuum to a plenum. These things, therefore, happen, so far as the media differ through which they are moved. But these, according to the excess of the things which are moved. For we see that things which have a greater momentum, either of weight or levity, if in other respects they possess similar figures, are more swiftly carried through an equal space, and that according to the ratio which the magnitudes have to each other. So that this also will be the case in passing through a vacuum. But this is impossible: for through what cause will it be more swiftly impelled? For in a plenum this necessarily happens; since that which is greater more swiftly divides by its force. And that which is borne along, or thrown, either divides by its figure, or by the momentum which it possesses. All things, therefore, will be moved with equal swiftness; but this is impossible. From what has been said, therefore, it is evident that if there is a vacuum the contrary will happen to that through which those who say there is a vacuum endeavour to prove its existence; for these fancy there is a vacuum separate and per se, if there is motion according to place. But this is just the same as to say that there is a certain separate place; and that this is impossible, has been already shown.
