Since, however, that which moves always moves something, and in something, and as far as to something (but I say in something, because it moves in time; and as far as to something, because it moves through a certain quantity of length; for it always at the same time has moved and moves; so that the thing which has been moved will be a certain quantity, and in quantity): if, therefore, A is that which moves, but B that which is moved; the length through which it is moved C, and the time in which it is moved D; in an equal time indeed, an equal force A will move the half of B through a length the double of C; but it will move through the length C in half the time D: for thus there will be proportion. And if the same force moves the same weight in this time through such a length, it will move through half the length in half the time; and half the force will move half the weight in an equal time, through an equal space. Thus, let the half of the force A be E, and let the half of the weight B be F; they will, therefore, be similarly affected, and the force will be analogous to the weight; so that they will move through an equal space in an equal time. And if E moves the weight F in the time D, through the length C, it is not necessary that E should move in an equal time, the double of the weight F, through half’ the length C. If, therefore, A will move the weight B in the time D through the length C; the half of A, i.e. E, will not on that account move the weight B in the time D; nor in a certain part of the time D will it move through certain part of the length C, or which has the same ratio to the whole length C, as the force A to the force E: for, in short, it may happen that it will move through no part of the space; for, if the whole force moves through so much length, half the force will not on that account move through as much length, nor in any time; since, if this were admitted, one man might move a ship, if the force of those who draw it should be numerically divided, and should also be divided into the length through which all those that draw the ship move. Hence, the assertion of Zeno is not true, that any part whatever of a grain of millet emits a sound; for nothing hinders this from moving in no time the air, which the whole bushel, in falling, moved. Neither, therefore, will this part of the grain of millet move as great a part, if it is by itself, as it moved together with the whole; since neither is any part in the whole, unless in capacity. But if there are two things, and each of these moves each of the weights, through so much space in so much time, the conjoined forces also will move that which is composed from the weights, through an equal length, and in an equal time; for there is proportion. Is, therefore, this also the case in change according to quality and increase? For there is something which increases, and something which is increased. But in so much time, and according to so much magnitude, the one increases, and the other is increased. That also which changes in quality, and that which is changed in quality, in a similar manner according to something, or according to some quantity, are more or less changed in quality; and also in so much time; the double in a double time, and in a double time the double; the half in half the time, or in half the time the half, or the double in an equal time. But if that which changes in quality or increases, either increases or changes so much in so much time, it is not necessary that the half also should increase or change in quality in half the time, and in half the time the half; but perhaps it will change in quality or increase in no part, as is the case in weights.
