内容 第9卷 · 269
命题 Propositio IX.28
If an odd number by multiplying an even number make some number, the product will be even.
若奇数乘以偶数，则其积为偶数。
奇数 A 乘偶数 B 得 C：C 由 A 个 B 相加而成，每个 B 为偶，故 C 由若干偶数之和构成，由 IX.21，C 为偶数。
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分步证明Step-by-step proof
1 / 4For let the odd number A by multiplying the even number B make C; I say that C is even.
设奇数A乘以偶数B得C，则C由与A中单位数相等的若干B相加而成。
For, since A by multiplying B has made C, therefore C is made up of as many numbers equal to B as there are units in A.
由于B是偶数，故C由若干偶数相加而成。
[VII. Def. 15] And B is even; therefore C is made up of even numbers.
根据第九卷命题21，任意多个偶数之和为偶数。
But, if as many even numbers as we please be added together, the whole is even.
因此C是偶数。
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