399 I will first show, by a demonstration entirely similar to the one by which Aristotle tried to demonstrate that motion in a void would happen in an instant, that motions do not observe with one another, with regard to speed, the ratio of the subtleties of the media; then, I will also show what ratio they do observe, so that the truth be more clearly known.
Thus if, as he himself said, the speed [in one medium] to the speed [in another] has the same ratio as the subtlety of [the first] medium to the subtlety of the other, let there be a mobile o; and let there be two media a, b, of which a is, for example, water, and b air; {1} also let the subtlety of air, which is 8, be greater than the subtlety of water, which is 2; and let the mobile float, not sink in water, but in air let its swiftness be as 4; and as the subtlety of air b, which is 8, is to the subtlety of water a, which is 2, let the swiftness in air, which has been assumed to be 4, be to another swiftness, which, of course, will not be zero, but 1.And so, since mobile o in subtlety b is moved with a swiftness of 4; and the swiftness of 4 is to the swiftness of 1, just as the subtlety of b is to the subtlety of a; it is thus manifest that the swiftness of mobile o in subtlety a will be as 1: however it has been assumed to be zero; which is unacceptable.Therefore speed will not be to speed as subtlety is to subtlety, as Aristotle assumed.
But I think it would be good to bring forth another demonstration. For let the conditions be the same as above; and let the subtlety of b be as 16, and the subtlety of a as 4; and let mobile o not be moved in a, but let it float; and let the swiftness of the same mobile in medium b be as 8. Again let there be another speed, which is as 1; and let the subtlety of b have the same ratio to the subtlety of another medium, c, as the swiftness 8 is to the swiftness 1: the subtlety of c will then be as 2.And since speed 8 is to speed 1 as the subtlety of b is to the subtlety of c, mobile o in subtlety b is moved with swiftness 8; therefore the same mobile o in the subtlety c will be moved with a swiftness as 1. That is, o will be moved in medium c: but medium c is thicker than medium a (for the subtlety of medium a, 4, is greater than the subtlety of c, which is as 2); now it has been assumed that in medium a mobile o is not moved: consequently mobile o will be moved through a thicker medium, but not at all through a more subtle one: which is most absurd and entirely unworthy of Aristotle.
It is thus evident that the speeds of motions do not observe with one another the ratios of the subtleties of the media. But in order that it may be known what ratios they observe, let us take {1} the true cause of the slowness and the swiftness of motion of the same mobile; which, as we have demonstrated above, is the lightness or heaviness of the medium with respect to that of the mobile. Let there be a mobile a, and a medium c, twice as light as medium b: certainly the time during which a is moved through b will not be twice the time during which a is moved through c; that is, the swiftness in [medium] c will not be twice the swiftness in b. {1}For let {1} d be the time in which a is moved through b itself; and let e be the time in which a is moved through c.And since the swiftness of a in the space of b will be equal to the excess by which the heaviness of a exceeds the heaviness of b, as demonstrated above; if the heaviness a is 20, but the heaviness of b is 8, the swiftness d {1} will certainly be 12: but, for the same reason, if the heaviness of c is 4, the swiftness e will be as 16: hence the swiftness e will not be twice the swiftness d. Therefore, since spaces b, c are equal in length, the time d will not be twice the time e.It is thus evident that the speed in medium c is not as great as Aristotle wanted it to be, but that it is much smaller: for, according to his way of thinking, the speed e would have to be, in consideration of speed d, 24; actually it is 16. It is therefore manifest that the lighter the medium, the faster the motion due to heaviness will be. But because speed always stands to speed in a lesser ratio than rareness to rareness, it follows that, when the rareness of the plenum stands to the rareness of the vacuum in the greatest of all ratios, it is not the case that the speed in the plenum must observe the same ratio with the speed in a void, as Aristotle falsely thought.