261 through more subtle media: which is certainly false; for many are the mobiles which are moved with a natural motion faster in thicker media than in more subtle ones, as, for example, in water than in air. For if we take as an example a very thin inflated bladder, it will in air go down slowly with a natural motion; but if it is let go from deep in water, it will fly very swiftly upward, again with a natural {1} motion. But at this point I know that someone may retort that the bladder in air certainly is moved and is carried fast downward; but in water, not only it does not go down more swiftly, but it does not even go down. To this I would reply, on the contrary, that the bladder in water is carried upward very swiftly, but then in air it is not moved. But, in order not to prolong the dispute, I say that in more subtle media it is not every motion that comes about faster, but only motion downward; and motion upward is swifter in thicker media. And it is certainly reasonable that this happens: for it is necessary that where motion downward takes place with difficulty, motion upward takes place with ease. It is consequently manifest that Aristotle's statement that the slowness of natural motion comes about because of the thickness of the medium was inadequate. Consequently, having abandoned his opinion, in order that we may bring forth the true cause of the slowness and the swiftness of motion, care must be taken that swiftness is not separated from motion: for he who assumes motion, necessarily assumes swiftness; and slowness is nothing other than lesser swiftness. Consequently, swiftness comes from the same thing as does motion: and so, since motion comes from heaviness and lightness, it is necessary that slowness or swiftness come from the same thing; from a greater heaviness of the mobile comes a greater swiftness of that motion which happens because of the heaviness of the mobile, that is, motion downward; and from a lesser heaviness, a slowness of that same motion; and, on the other hand, from a greater lightness of the mobile will emanate a greater swiftness of that motion which happens because of the lightness of the mobile, namely motion upward. It is consequently manifest how diversity in swiftness and in slowness of motion comes about in different mobiles in motion in the same medium: for if the motion is downward, what is heavier will be moved more swiftly than what is less heavy: but if the motion is upward, what is lighter will be moved faster. But whether two mobiles carried in the same medium observe the same ratio in the swiftness of their motions as there is between their heavinesses, as Aristotle believed, will be examined below. {1} Next, concerning the swiftness and slowness of the same mobile in different media, it happens, similarly, that a mobile is moved more swiftly [262] downward in that medium in which it is heavier, than in another in which it is less heavy; and it goes up more swiftly in that medium in which it is lighter, than in another in which it is less light. {1} Hence it is manifest that, if we find in what media the same mobile will be heavier, the media will have been found in which it will go down more swiftly; but if, on the other hand, we demonstrate how much heavier the same mobile is in this medium than in that one, it will also have been demonstrated how much more swiftly it will be moved downward in this medium than in that one: and, by examining the light in converse fashion, when we find in which medium the same mobile will be lighter, a medium will have been found in which the mobile will go up more swiftly; but if we discover by how much the same mobile is lighter in this medium than in that one, it will then have been discovered how much more swiftly the mobile will go up in this medium than in that one. But, in order that all these things may be grasped with more exactitude in the case of any particular motion, treating first of all those motions that are made by different mobiles in the same medium, we will show what ratio their motions observe with one another, with respect to slowness and swiftness; next, inquiring about motions that are made by the same mobile in different media, we will similarly demonstrate what ratio they observe in motions of this sort.
Chapter 8 [262.19-273.31] In which it is demonstrated that different mobiles moving in the same medium observe another ratio than the one attributed to them by Aristotle.
In order, then, that the things that must be thoroughly studied may be dealt with more easily, one must, in the first place, consider that {1} difference between two mobiles can happen in two ways: for either they are of the same species, as, for example, both lead, or both iron; and they differ in size: or they are of different species, e.g. one iron, the other wood; they then differ from one another either in size and heaviness, or in heaviness and not in size, or in size and not in heaviness. Concerning those mobiles that are of the same species Aristotle has said, that