as much less as the swiftness in medium c is less than the swiftness in medium b: now the swiftness of medium b has been assumed to be eight times that of the swiftness in medium c: hence the subtlety of medium b also will be eight times that of the subtlety of medium c: that is why the subtlety of this c will be 2. </s>
<s id="id.1.1.8.09.05">Therefore mobile o is moved with swiftness 1 in the subtlety of medium c, which is of 2; but it has been assumed that it is not moved in the subtlety of medium a, which is of 4: hence mobile o will not be moved in the greater subtlety, although it is moved in a lesser subtlety: which is most absurd. </s>
<s id="id.1.1.8.09.06">It is thus evident that, the speeds of motions do not observe with one another the ratios of the subtleties of the media. </s>
<s id="id.1.1.8.09.07"> But, apart from any other demonstration, can anyone fail to see the falsehood of Aristotle's opinion? </s>
<s id="id.1.1.8.09.08">For if the motions observe the ratio of the media, then, conversely, the media will also observe the ratio of the motions: thus since wood goes down in air but in water not at all, and, consequently, motion in air has no ratio to motion in water, therefore also the rareness of air will have no ratio to the rareness of water: what can be more absurd than this? </s>
<s id="id.1.1.8.09.09">But lest someone might think he had sufficiently answered my argument, if he said "Though wood is not moved downward in water, it is however moved upward, and the ratio that the upward motion has in water to the downward motion in air, is the same as that of the rareness of water to the rareness of air", and with this he might think he had cleverly saved Aristotle -- we will do away with this subterfuge also: namely, by taking a body which in water is moved neither upward or downward, such as, for example, water itself, which however is moved quite fast in air. </s>
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<s id="id.1.1.8.10.00"/>
<s id="id.1.1.8.10.01">Thus then, Aristotle's way of thinking having been with reason ranked in second place, let us now inquire about the ratio that the motions of the same mobile done in different media observe; and, in the first place, let us show concerning upward motion, that solid magnitudes lighter than water, having been impelled into water, are carried upward with as much force, as that by which a quantity of water, whose size is equal to the size of the submerged magnitude, will be heavier than that magnitude.</s>
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<s id="id.1.1.8.11.00.fig"/>
<s id="id.1.1.8.11.01">And thus let the first position of the water, before the magnitude is submerged in it, be along surface ab; and let the solid magnitude cd be forcibly submerged in it; and let the water be raised to the surface ef: and since water eb, which is raised, has a size equal {1} to the size of the whole submerged magnitude, and the magnitude is assumed to be lighter than water, the heaviness of water eb will be greater than the heaviness of cd. </s>
<s id="id.1.1.8.11.02">Then let it be understood that tb is that part of the water, whose heaviness is equal to the heaviness of magnitude cd: accordingly it must be demonstrated that, magnitude cd </s>
