But that there may be a certain infinite motion, one and continued, and that this is a circular motion, we shall now assert. For every thing whieh is locally moved, is either moved in a circle, or in a right line, or in that which is mixed ftom both these: hence if neither of these motions is continued, neither can that be continued which is composed from both of them. But that a thing which is locally moved in a finite right line, cannot be moved continually, is manifest. For to do this it must return; but that which returns in a right line, is moved with contrary motions. For the motion upward is contrary to the motion downward, according to place; the motion to the anterior, to thlat which is to the posterior part; and the motion to the right hand, to that which is to the left. For these are the contrarieties of place. But what the motion is which is one and continued, has been before defined, viz. that it is of one thing, and in one time, and in that which has no difference according to form. For there are three things, viz. that which is moved, as man or God; when, as time; and the third thing, that in which the motion is produced; and this is place, or passive quality, or form or magnitude. But contraries differ in species, and are not one. And the differences of place are those which have been enumerated. But this is an indication that that the motion from A to B is contrary to the motion from B to A, that they stop and cause each other to cease, if they are produced at the same time. The like also takes place in a circle; for instance, the motion from A to B is contrary to the motion from A to C; for they will stop each other though they are continued, and there will not be a regression, because contraries corrupt and impede each other. Motion however, to that which is oblique is not contrary to that which is to the upward place. But it is especially evident, that it is impossible for the the motion in a right line to be continued, because that which returns must necessarily stop, not only if it is moved in a right line, but also if it is moved upon a circle. For it is not the same thing to be moved in a circle, and upon a circle; since that which is moved at one time continues its motion, and at another, when it has arrived at the same thing from which it began to be moved, again returns. But that it is necessary it should stop, is not only rendered credible by sense, but also by reason.
But the principle is this; for since there are three things, the beginning, middle, and end; the middle compared with each of theae is both; and in number indeed it is one, but in definition two. Besides, it is one thing to be in capacity, and another to be in energy. Hence any point whatever of a right line, vhich is between the extremes, is in capacity indeed the middle, but is not in energy unless it divides the line, and having stood still, again begins to be moved; but thus that which was the middle becomes the beginning and end, tho beginning indeed of the posterior, but the end of the prior motion. I say, for instance, if A which is locally moved, should stand still at B; and again should be moved to C. But since it iit continually moved, the point A can neither have approached to the point B, nor have. receded from it; but can ouly be in the now, and not in any time, except in that while time, of which that moment or now is the division. If any one, however, asserts, that it has approached and receded; A which is locally moved, will ahvays stand still. For it is impossible for A to have at the same time approached to B, and receded from it: it will, therefore, be in another and another point of time. Hence that will be time which is in the middle; so that A will rest in B, and in a similar manner it will also rest in the other points; for the same reasoning applies to all of them. But since that which is locally moved, viz. A, uses B as the middle, end, and beginning, it is necessary that it should stop, because it makes two things, just as if it should be mentally conceived. But it recedes from the point A, i.e., from the beginning, but accedes to C, when it has finished its motion and stood still. Hence this must be be said in answer to the doubt: for it has this doubt. For if the line A is equal to the line F, and A is continually moved from the extremity to C, but at the same time A is in the point B, and D is moved from the extreme line F to G equably, and with the same celerity with which A is moved; certainly D will arrive at G, before A will have arrived at C. For that which was first impelled, and which first departed, must necessarily have arrived the first. A therefore did not at the same time accede to B, and recede from it; and hence it arrived later at the end: for if it had receded at the same time, it would not have arrived later; but it is necessary that it should have stood still. It must not, therefore, be admitted, that when A approaches to B, D is at the same time moved from the extreme F; for if A approaches to B, it will also recede, and not at the same time. But it was in a section of time, and not in time. Here therefore it is impossible thus to speak, viz. in that which is continued: but in that which returns, it is necessary thus to speak; for if G were moved to D, and again having receded was carried downward, certainly it has in this case, used D as the beginning and end, viz. one point as two. Hence it is necessary that it should have stood still, and not at the same time have approached to D, and receded from D; for at once it would be there, and would not be in the same now. The solution however formerly given, is not to be adduced here; for it cannot be said, that G is in D in a section of time, and that it has neither approached nor receded; for it is necessary that it should arrive.at an end which is in energy, and not in capacity. The point therefore which is in the middle is in capacity; but this is in energy. And it is indeed the end downward, but the beginning from above. After the same manner therefore, there is an end and beginning of motions. Hence it is necessary that that which returns upon a right line should stand still; and therefore it is not possible that there can be a continued perpetual motion upon a right line. After the same manner a reply must be made to those who ask the question of Zeno, and who demand whether it is always necessary to pass through the half: for these say they are infinite; and it is impossible to pass through infinites. Or as some in a different manner make the same inquiry, who require it to be granted them, that together with the half being first moved through, every half also may be numbered as it is generated. Hence, when the moveable thing has passed through the whole line, it will happen that an infinite number will be numerated. But this is confessedly impossible. In the first discussions, therefore, concerning motion, we solved this argument, through time containing in itself infinites; for there is nothing absurd in admitting, that something may pass through infinites in an infinite time; but the infinite is inherent in length and in time, in a similar manner. This solution indeed is sufficient in answer to the interrogator; for it was asked, whether infinites could be passed through, or numerated in a finite time. But this solution is not sufficient so far as pertains to the thing, and to truth: for if any one dismissing length and the interrogation whether infinites can be passed through in a finite time, makes these enquiries about time itself, (for time has infinite divisions) this solution will be no longer sufficient. But the truth which we mentioned a little before must be asserted: for if any one divides a continued line into two halves, he uses one point as if it were two; since he makes it both a beginning and end. He also does this who numerates, and who divides into halves. But thus dividing, neither a line nor motion will be continued: for continued motion is of that which is continued. And in the continued there are infinite halves, yet not in energy, but in capacity. But if the motion should make them in energy, it will not be continued, but will stand still; which evidently happens to him who numbers the halves; for it is necessary that he should numerate one point as if it were two: for it will be the beginning of one half, and the end of the other, if he does not numerate one continued line, but two halves. Hence to him who asks, whether infinites can be passed through, either in. time, or in length, we must reply, that this is partly possible, and partly not: for it is not possible for infinites in energy to be passed through, but it is possible for infinites in capacity: for he who is continually moved passes through infinites accidentally, but simply does not: for it happens to a line that there are infinite halves; but the essence and being are different. It is also evident that unless the point of time by which prior and posterior are divided, is always attributed to the posterior, the thing itself being considered, the same thing will be at the same time being and non-being, and when it will be in generation, or becoming to be, will not be in generation. The point, therefore, is common to both the prior and posterior, and is one and the same in number, but is not the same in definition; for it is the beginning of the one, and the end of the other. But so far as pertains to the thing it is always of the posterior passive quality: for let the time be A B C; the thing D. This in the time A is white, but in the time B is not white. Hence in C it is white and not white: for in any point of A, it would be true to say, it is white if it was white in all this time; and in B not white. But C is in both. It must not, therefore, be granted that it was white in the whole time, but the last now or moment C must be excepted: and this is now posterior. And if it should become not white, and the white should be corrupted in the whole of A; it is generated or is corrupted in C. Hence, it is true to say, that it is first white, or not white in that; or when it is generated, it will not be; and when it is corrupted it will be; or it is necessary, that it should be at the same time white and not white, being and non-being. But if it is necessary that a thing which before before was non-being should become being, and when it is becoming to be it is not, — if this be the case, time cannot be divided into indivisible times: for if D was becoming to be white in the time A, and at the same time is made white, and is in another indivisible adhering time, i.e. in B; if it was becoming to be in A, but is in B, it is necessary that there should be a certain intermediate generation; so that there was time in which it was generated: for the same reasoning will not apply to those who say there are not indivisible times; but in the last point of the time in which it was becoming to be, it was generated and is; to which point nothing adheres, nor is successive. But if there are indivisible times, they will be successive. It is evident, therefore, that if it was generated in the whole time A, there is not a greater time in which it was becoming to be, and was generated, than that in the whole of which it was alone generated. These, therefore, and such as these are the arguments which some one may believe in, as appropriate. But to those who consider the affair logically, from these arguments also, it may appear that this very same thing may happen: for every thing which is continually moved, if it is not impeded by any thing, was first moved to that to which it arrives by lation. Thus if it arrives at B, it was also moved to B; and not then only when it was near, but immediately as soon as it began to be moved: for why now rather than before? The like also takes place in other things. But that which is moved from A to C, will again come to A, when it is moved continually. When, therefore, it was moved from A to C, it was then also moved with the motion from C. Hence it is at the same time moved with contrary motions: for the motions are contrary which are upon a right line. At the same time also, it changes from this, in which it is not. If, therefore, this is impossible, it is necessary that it should stand still in C: and hence there is not one motion; for the motion which is intercepted by standing still is not one. Farther still, from these things also, it is more universally evident concerning all motion: for if every thing which is moved, is moved with some one of the above-mentioned motions, it will also rest with some one of opposite rests; for there is not any other besides these. But that which is not always moved with this motion (I mean motions which are different in species, and not if any thing is a part of the whole), it is necessary first to rest with an opposite rest: for rest is the privation of motion. If, therefore, the motions are contrary which are made through a right line, and it is not possible for any thing to be moved at the same time with contrary motions; that which is moved from A to C, cannot at the same time also be moved from C to A. Since, however, it is not at the same time moved, but is moved with this motion, it is necessary that it should have rested before in C: for this is the rest opposite to the motion from C. From what has been said, therefore, it is evident that the motion is not continued. Besides, this reasoning is more appropriate than what has been before said: for that which is not white, is at the same time corrupted, and becomes white. If, therefore, the alliation into white and from white is continued, and does not remain for any time; that which is not white will at the same time be corrupted, and become white, and become not-white: for there will be the same time of three things. Again, it does not follow that if time is continued, motion also is continued; but it is successive. But how can the same thing be the extreme of contraries, as of whiteness and blackness? The motion, however, which is made upon a periphery is one and continued; for nothing impossible happens: for that which is moved from A, is at the same time moved to A, according to the same impetus; for to that to which it comes, to this also it is moved. It is not, however, moved at the same time with contrary or opposite motions: for not every motion which is from this, is contrary to that which is to this, or oppesite. But that motion is contrary which is made upon a right line: for to this there are contraries according to place; for instance, the motion through a diameter; since this is very much distant. But that motion is opposite which is made through the same length. Hence nothing prevents that which is moved in a periphery from being continually moved, and not failing at any time: for the motion in a circle is from the same to the same; but the motion through a right line is from the same to another. The motion in a circle also is never in the same things, but that in a right line is frequently in the same. Hence that which always becomes in another and another, maybe moved continually; but that which is frequently in the same things may not: for it is necessary to be at the same time moved with opposite motions. Neither, therefore, in a semicircle, nor in any other periphery, is it possible to be moved continually: for it is necessary frequently to be moved through the same things, and to be changed with contrary mutations: for it does not conjoin the end with the beginning; but the motion of a circle conjoins these, and is alone perfect. It is also evident from this division, that neither can any other motions be continued: for in all of them it happens to be often moved through the same things; as, for instance, in alliation, through intervening media: in the motion of quantity, through middle magnitudes; and in a similar manner, in generation and corruption: for it is of no consequence, whether those things are made few or many, in which the mutation takes plaee; nor whether any thing intermediate is added or taken away; for it happens in both ways frequently to be moved through the same things. From hence, therefore, it is evident that neither do those physiologists speak well who say, that all sensible natures are always moved: for it is necessary that some of these motions should be moved; and according to these, alliation especially takes p1ace: for they say that all things flow, and are diminished; and besides this, they call generation and corruption alliation. But the arguments now employed, universally show of all motion that it is not possible to be continually moved with any motion, except that which is circular; so that it is not possible to be continually moved, either according to alliation, or according to increase. This much, therefore, has been said by us to prove that there is neither any infinite mutation, nor any continued motion, except that which.is in a circle.
