double the lightness of b); however the swiftness 14 is less than double the swiftness 8.</s>
<s id="id.1.1.10.07.04">But swiftness 14 certainly has the same ratio, arithmetically, to swiftness 8 as the lightness of d to the lightness of b; since the excess of 14 over 8 is 6, and 6 is also the excess of the lightness of d, 12, over the lightness of b, 6. </s>
<s id="id.1.1.10.07.05">But if medium de should be lighter, in such a way that the heaviness of this d is 5, then the swiftness f will be 15 (for the excess of the heaviness of mobile a over the heaviness of medium d will be 15); and, again, swiftness 15 will be to swiftness 8 in the same ratio as the heaviness of medium b, 12, to the heaviness of medium d, 5, that is, the lightness of d to the lightness of b: for the excess in both cases will be 7. </s>
<s id="id.1.1.10.07.06"> If, on the other hand, the heaviness of d is only 4, the swiftness f will be 16; and swiftness 16 will be to swiftness 8 (whose excess is 8) similarly in the same arithmetic ratio as the heaviness of b, 12, to the heaviness of d, 4, that is, the lightness of d to the lightness of b, whose excess is similarly 8. </s>
<s id="id.1.1.10.07.07">Now if, again, medium de is lighter and the heaviness of d is only 3, then the swiftness f will be 17; and the swiftness f, 17, will be to swiftness 8 (whose excess is 9) in the same arithmetic ratio as the heaviness of b, 12, to the heaviness of d, 3, that is, the lightness of d to the lightness of b. </s>
<s id="id.1.1.10.07.08">And if, again, medium de is lighter and the heaviness of d is only 2, then the swiftness f will be 18; and its arithmetic ratio to the swiftness 8 will be the same as that of the heaviness of b, 12, to the heaviness of d, 2, that is, of the lightness of d to the lightness of b: for the excess in both cases will be 10. </s>
<s id="id.1.1.10.07.09">If, again, medium de is lighter and the heaviness of d is only 1, then the swiftness f will be 19; it will have the same arithmetic ratio to swiftness 8, as the heaviness of b, 12, has to the heaviness of d, 1, that is, the lightness of d to the lightness of b: for the excess in both cases will be 11. </s>
<s id="id.1.1.10.07.10">And if, finally, the heaviness of d is 0, so that the excess of the heaviness of mobile a over medium d is 20, the swiftness f will be 20; and swiftness f, 20, will be to swiftness 8 in the same ratio, arithmetically, as that of the heaviness of b, 12, over the heaviness of d, 0: for in both cases the excess will be 12. </s>
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<s id="id.1.1.10.08.00"/>
<s id="id.1.1.10.08.01">It is therefore evident how it is not geometrically but arithmetically that swiftness observes to swiftness the ratio that the lightness of the medium has to the lightness of the medium: and since it is not absurd, in an arithmetic ratio, that a quantity be to a quantity as a quantity to nothing, it will </s>
