If an odd number measure an even number, it will also measure the half of it.
如果一个奇数度量一个偶数，那么它也度量该偶数的一半。
奇数 A 量度偶数 B：设 A 量 B 得 C 次。假设 C 为奇，则 B 为奇数（IX.29），矛盾；故 C 为偶，即 A 以偶次量 B，从而 A 也量 B 的半。
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For let the odd number A measure the even number B; I say that it will also measure the half of it. For, since A measures B, let it measure it according to C; I say that C is not odd.
设奇数A度量偶数B，则存在数C使得A乘以C等于B。
For, if possible, let it be so. Then, since A measures B according to C, therefore A by multiplying C has made B.
假设C是奇数，则B由奇数个奇数相乘得到，故B为奇数，与假设B为偶数矛盾。
Therefore B is made up of odd numbers the multitude of which is odd. Therefore B is odd: [IX. 23] which is absurd, for by hypothesis it is even.
因此C不是奇数，故C为偶数。
Therefore C is not odd; therefore C is even. Thus A measures B an even number of times.
所以A以偶数次度量B，即A度量B的一半。