But motion is divisible in a twofold respect; in one way by time; in another, according to the motions of the parts of that which is moved. Thus, if the whole A C is moved, the part also A B will be moved, and the part B C. Let, therefore, D E be the motion of the part A B, and E F, the motion of the part B C. Hence it is necessary that the whole D F should be the motion of AC: for it will be muved according to this motion; since each of the parts is moved according according to each, and nothing is moved according to the motion of another thing. So that the whole motion is the motion of the whole magnitude. Farther still, if all motion is the motion of something; but the whole motion D F is neither the motion of either of the parts, (for each part is the motion of each part) nor of any tbing else, (for where there is a whole motion of the whole of a thing, the parts of that motion will be the motions of the parts of the thing; but the parts of the motion D F are the motions of the parts A B C, and not of other things; for there is not one motion of many things; if tbis be the case, the whole motion will be the motion of the magnitude A C. Besides, if there is another motion of the whole, as for instance H I, the motion of each of the parts will be taken from it; but these will be equal to the motions D E, E F; for there is one motion of one thing. So that if the whole motion H I, is divided into the motions of the parts, the motion H I, will be equal to the ·motion D F. But if any thing remains, as for instance K I, this will not be the motion of any thing: for it will neither be the motion of the whole, nor of the parts, because there is one motion of one part; nor will it be the motion of any thing else, because the motion of any continued quantities is continued. This also will be the case, if it should surpass according to division. So that if this is impossible, it is necessary that it should be the same and equal. This, therefore, is the division according to the motions of the parts, and it is necessary that it should be the division of every thing which consists of parts. But another division takes place, according to time: for since all motion is in time, all time is divisible, and there is less motion in a less time; it is necessary that all motion should be divided according to time.
