assume that the different mobiles of which we speak differ only in heaviness, though they are equal in size; so that you would not perchance say: Let there be, for example, a mobile [a] whose heaviness [in air {1}] is 8; and let the heaviness of an amount of water equal in size to the said mobile be 3; then it is manifest, from the things that have been said, that the swiftness [in water] of the said mobile will be as 5: but if you take another mobile, such as c, whose size were twice that of a, and whose heaviness [in air] were less than twice the heaviness of a, namely 12, and the heaviness of an amount of water equal in size to c were 6, then the swiftness [in water] of c would be as 6.</s>
<s id="id.4.0.0.96.11">However, it must not be said that c will go down faster than a; because then the ratio would no longer hold good, since the mobiles differ in size. </s>
<s id="id.4.0.0.96.12">Bu if we want the ratio to hold good, let us take half of c, so that its size is equal to the size of a; then the heaviness of c [in air] will be 6: but the heaviness [of an amount] of water [equal to] half [the size of c] will be 3, so that the speed of half of c will be 3, as compared with the speed of a, which will be 5: therefore a will go down faster than the whole of c (for the whole is moved with the same swiftness as its half). </s>
<s id="id.4.0.0.96.13">Therefore it will be true to say, that the swiftness of a is 5 as compared to the swiftness of half of c, which will be 3; or else that the swiftness of the whole of c is 6 as compared to the swiftness of the double of a, which will be 10. </s>
<s id="id.4.0.0.96.14">Hence it is evident that when we reason on the subject of the swiftness or the slowness of mobiles, it is necessary to have in mind those mobiles whose difference depends solely on heaviness, although they are equal in size. </s>
<s id="id.4.0.0.96.15">Then when the ratio of the speeds to one another has been found, the same ratio will be observed between mobiles of the same kind, no matter how much they may differ in size {1}: for a piece of lead whose heaviness is 10 pounds goes down with the same speed as a piece of lead whose heaviness is 100 pounds. </s>
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<s id="id.4.0.0.97.00"/>
<s id="id.4.0.0.97.01"> DO. This seems truly astonishing, and is contrary to Aristotle's opinion. </s>
<s id="id.4.0.0.97.02">It will indeed be difficult for me to believe it, unless you somehow convince me.</s>
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<s id="id.4.0.0.98.00.fig"/>
<s id="id.4.0.0.98.01">AL. The demonstrations brought forth above should be sufficient to convince you of this; {1} even if they do not explicitly demonstrate this, it nevertheless depends on them: but, if they are not sufficient for you, I will bring forth </s>
