265 the other, the combination of the two is moved more slowly than that part which was moved faster than the other, but more swiftly than the remaining part, which, alone, was carried more slowly than the other: {1} as, for example, if we understand two mobiles, such as a piece of wax and an inflated bladder, both of which are carried upward from deep water, but the wax more slowly than the bladder, we ask that it be conceded, that if they are combined, the combination will go up more slowly than the bladder alone, but more swiftly than the wax alone. Indeed this is very clear: for who doubts that the slowness of the wax will be diminished by the speed of the bladder, and, on the other hand, that the speed of the bladder will be retarded by the slowness of the wax, and that a certain motion intermediate between the slowness of the wax and the speed of the bladder will result? Similarly, if on the other hand two mobiles go down, one of which is carried more slowly than the other, as, for example, if one is wood, the other a bladder, which go down in air, the wood more swiftly than the bladder, we presuppose this: if they are combined, the combination will go down more slowly than the wood alone, but more swiftly than the bladder alone. For it is manifest that the swiftness of the wood will be retarded by the slowness of the bladder, while the slowness of the bladder will be accelerated by the speed of the wood; and similarly a certain motion intermediate between the slowness of the bladder and the swiftness of the wood will result.
Let there be two mobiles of the same species, the larger a, and the smaller b; and, if it can be done, as our adversaries hold, let a be moved more swiftly than b. There are then two mobiles one of which is moved more swiftly than the other; hence, according to what has been presupposed, the combination of the two will be moved more slowly than the part, which alone, was moved more swiftly than the other. If then a and b are combined, the combination will be moved more slowly than a alone: but the combination of a and b is larger than a alone: hence, contrary to our adversaries' view, the larger mobile will be moved more slowly than the smaller; which would certainly be unsuitable. {1}What clearer indication do we require of the falsehood of Aristotle's opinion? But, I ask, who will not recognize the truth of this on the spot, when he examines it in a pure and simple and natural way?For if we presuppose that the mobiles a and b are equal and that they are very near each other, then, by the consensus of all, they will be moved with equal swiftness: and if we understand that while they are being moved, they are joined, why, I ask, will they double the swiftness of their motion, as Aristotle held, or increase it? Accordingly, let it be sufficiently confirmed that there exists no cause, per se, why mobiles of the same species should be moved with unequal speeds, but there certainly is one why they should be moved with equal speed. But if there were some accidental cause, such as, for example, the shape of the mobile, it must not be classified amongst the causes per se: and moreover, the shape helps or hinders the motion but little, as we shall show in the proper place {1}. Also, one must not , as many are in the habit of doing, immediately revert to extremes, {1} by taking, for example, a piece of lead of very large size, and, on the other hand, a tiny blade or a leaf of the same lead, which sometimes will even float on water: for since there is a certain cohesion and (so to speak) a tenacity and a viscosity of the parts of air as well as of water, this cannot be overcome by a very small heaviness. Accordingly, the conclusion must be understood as concerning those mobiles where the heaviness and size of the smaller one is large enough that it is not hindered by that small tenacity of the medium; such as, for example, a leaden ball of one pound. Moreover, as for scoffers of this kind, who perhaps persuade themselves that they can defend Aristotle, what happens to them if they revert to extremes, is this: the greater the difference between the mobiles that they choose, the more they will have to toil. For if they take a mobile that is a thousand times larger than the other, before they show that one surpasses the other a thousand times in speed, it will undoubtedly cost them sweat and toil.
But, in order to come to the things that remain, it follows now that we should see what ratio mobiles of different species, moved in the same medium, observe in their motions. Such mobiles can differ from one another in three ways; for either they differ in size and not in heaviness, or they differ in heaviness and not in size, or they differ in size and in heaviness; it is necessary to inquire only about those that differ in heaviness and not in size. For the ratios of those that differ in the other two ways can be reduced to this one: thus if the mobiles differ in size and not in heaviness, if from the larger a part is taken that is equal to the smaller, then the mobiles will differ in heaviness and not in size; and this part, taken away from the larger mobile, will observe the same ratio with the other mobile, as the ratio that the whole