Zeno, however, paralogizes: for he says, if always every thing is either at rest or moved, when it is in a place equal to itself, (but that which which is borne along is always in the nows in a place equal to itself,) an arrow which is borne along is immoveable. But this is false: for time is not composed from nows which are indivisible, as neither is any other magnitude. There are, however, four arguments of Zeno concerning concerning motion; which afford some difficulty to those that solve them. The first attempts to prove that a thing cannot be moved, because it is necessary that what is borne along should arrive at the half before it arrives at the end; which argument we have already dissolved. The second is that which is called Achilles, and is this, that the slower, when it runs from the swifter, will never be overtaken: for, prior to this, it is necessary that the pursuer should arrive thither whence that which fled began to fly; so that it is necessary that the slower should always a little farther. But this argument is the same as that which bisects; though it differs in iiot bisecting the assumed magnitude. It is concluded, therefore, from the argument that the slower is not overtaken, but for the same reason with the bisection: for it happens in both, that the thing in motion does not arrive at the end, the magnitude, in a certain respect, being divided. In this also it is tragically added, that it will not by the most rapid pursuit overtake that which is slower. So that the solution is necessarily the same. To think, however, that the thing which precedes will not be overtaken, is false: for when it precedes it is not overtaken; but at the same time will be overtaken, if it is admitted that a finite space is passed through. These, therefore, are two of his arguments. But the third is that which was just now mentioned, that an arrow, which is borne along, stands till. This, however, is inferred from assuming that time is composed from nows; for this not being granted, there will not be a syllogism. But the fourth argument is concerning equal bulks which are moved in the stadium in a contrary direction, some from the end, and others from the middle of the stadium, with an equal celerity: in which he thinks it will happen that half the time will be equal to the double. The paralogism, however, consists in this, that Zeno thinks it should be granted, that one of these bulks, which passes by that which is in motion, and the other which passes by that which is at rest, are moved with an equal celerity, in an equal time, through an equal magnitude. But this is false. Thus, for instance, let the equal bulks A A A A stand still; but let the bulks BBBB begin to be moved from the middle of them A, since they are equal to these in number and magnitude; and let the bulks CCCC begin to be moved from the last, these also being equal in number and magnitude, and moved with the same celerity as B. It will happen, therefore, that the first B and the first C will be at the same time in the extremity A, since they are moved in a parallel direction. It will also happen that all C will pass through all A; but all B will pass through the half; so that the time also will be half: for each is equal parallel to each. At the same time too, it happens that all B will pass by all C (for at the same time the first C and the first B are in contrary extremes), since the same time is consumed in passing by each B, that is consumed in passing by each A, as Zeno says, because both are moved in an equal time parallel to all A. This, therefore, is his reasoning; which happens through the above-mentioned falsity. Neither, therefore, will there be any thing impossible in what we have asserted, from the mutation which is in contradiction; as if a thing should change from non-white into white, and into neither, that it will, therefore, neither be white, nor non-white: for it does not follow, that if the whole is not in either, that it will not be called white, or not white: for we call a thing white, or not white, not because the whole is such, but because most, or the principal of its parts, are white. And it .is not the same thing, not to be in this, and for ·the whole not to be in this. The like also takes place in being and non-being, and in other things which subsist according to contradiction: for the whole will not necessarily be in either of the opposites, but always in neither. Again, in a circle, and a sphere, and, in short, in things which are moved in themselves, it will happen that these will be at rest; for both they and their parts will be in the same place for a certain time; so that they will at the same time be at rest, and be moved. For first, the parts are in no time in the same place; and, secondly, the whole also always changes into another: for it is not the same circumference which is assumed from the point A, from the point B, and from the point C, and from each of the other points, except in the same manner as a musical man, and a man, are the same, because it so happens. So that the one will always change into the other, and will never be at rest. After the same manner the thing takes place in a sphere, and in other things which are moved in themselves.
