<s id="id.1.1.8.12.07">And an answer to the other question is also obtained, namely, what ratio different mobiles, equal in size, and unequal in heaviness, observe in the swiftness of their motions. </s>
<s id="id.1.1.8.12.08">For if each of them is carried upward with as much force as that by which an amount of the medium as great in size as the size of the mobile is heavier than the mobile itself, then, having subtracted the heavinesses of the mobiles from the heaviness of the aforesaid amount of the medium, the remaining numbers will observe with one another the ratio of the swiftnesses: if, for example, the heaviness of one mobile is 4, of the other 6, and of the medium 8, then the swiftness of the mobile whose heaviness is 4, will be 4, but the swiftness of the other will be 2. </s>
<s id="id.1.1.8.12.09">Now, these swiftnesses, 4 and 2, are not to one another as the lightnesses of the mobiles, which are 6 and 4 {1}: for the excesses of one number over two others will never be to one another as those two numbers; nor will the excesses of two numbers over another number be to one another as the exceeding numbers. {2}</s>
<s id="id.1.1.8.12.10">It is therefore very clear that in motion upward, the motions of different mobiles are not to one another as the lightnesses of the mobiles. </s>
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<p>
<s id="id.1.1.8.13.00"/>
<s id="id.1.1.8.13.01">It thus remains for us to show that also in the motion of mobiles downward the swiftnesses are not to one another as the heavinesses of the mobiles and, at the same time, to show what ratio the swiftnesses of the same mobile observe in different media; all these things will easily be drawn from the following demonstration. </s>
<s id="id.1.1.8.13.02">I say, then, that a solid magnitude heavier than water is carried downward with as much force as that by which a quantity of water, having a size equal to the size of the same magnitude, is lighter than this magnitude. </s>
</p>
<p>
<s id="id.1.1.8.14.00.fig"/>
<s id="id.1.1.8.14.01">Thus, let the first position of the water be along surface de; let the solid magnitude bl be released into the water, and let the water be raised up to surface ab; also let water ae be such that it has a size equal to the size of the same magnitude: and since the solid magnitude is assumed to be heavier than water, the heaviness of the water will be less than the heaviness of the solid magnitude. </s>
<s id="id.1.1.8.14.02">Then let ao be understood to be an amount of water that has a heaviness equal to the heaviness of bl: and since water ae is lighter than ao by the heaviness of do, it must be demonstrated that the magnitude bl is carried downward with a force as great as the heaviness of water do. </s>
<s id="id.1.1.8.14.03">Let another solid body be imagined, lighter than water, joined </s>
