for the excess of 20 over 12, which is 8, is the same as the excess of 8 over 0. </s>
<s id="id.1.1.10.05.05">That is why, if, as Aristotle wanted, the motions had to one another the ratio, geometrically, of subtlety to subtlety, he would correctly have concluded that in the void motion could not happen in time; for the time in the plenum to the time in the void cannot have the ratio of the subtlety of the plenum to the subtlety of the void, since the subtlety of the void is null: but if swiftness observed to swiftness the said ratio not geometrically but arithmetically, nothing absurd would follow. </s>
<s id="id.1.1.10.05.06"> But it is certainly true that swiftness observes to swiftness, arithmetically, the ratio of the lightness of the medium to the lightness of the medium; since since the swiftness in relation to the swiftness is, not as the lightness of the medium to the lightness of the medium, but, as has been demonstrated {1}, as the excess of the heaviness of the mobile over the heaviness of this medium to the excess of the heaviness of the same mobile over the heaviness of the other medium. </s>
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<p>
<s id="id.1.1.10.06.00"/>
<s id="id.1.1.10.06.01">In order that this be more apparent, here is an example. </s>
</p>
<p>
<s id="id.1.1.10.07.00.fig"/>
<s id="id.1.1.10.07.01">Let there be mobile a, whose heaviness is 20; let there be also two media, bc, de, unequal in heaviness; and let the size of b be equal to the size of a, and the size of d be similarly equal to the size of a; and, since we are now talking about downward motion taking place in the void, let the media be lighter than the mobile, and let the heaviness of b be 12, but the heaviness of d be 6: it is therefore manifest, from what has been demonstrated above, that the swiftness of mobile a in medium bc to the swiftness of the same mobile in medium de will be as the excess of the heaviness of this a over the heaviness of b to the excess of the heaviness of this a over the heaviness of d, that is as 8 to 14. </s>
<s id="id.1.1.10.07.02">Hence let the swiftness of a in medium bc be as 8, but let the swiftness of the same a in medium de be 14: {1}it is then apparent that swiftness 14 to swiftness 8 does not observe geometrically the ratio of the lightnesses of the media. </s>
<s id="id.1.1.10.07.03">For the lightness of medium de is double that of the lightness of medium bc (for since the heaviness of b is 12, but the heaviness of d is 6, that is since the heaviness of b is double the heaviness of d, the lightness of d will be </s>
