If a number by multiplying two numbers make certain numbers, the numbers so produced will have the same ratio as the numbers multiplied.
如果一个数乘以两个数得到两个乘积，那么这两个乘积的比等于被乘的两个数的比。
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正文图形由校订坐标生成；点、线、角、圆可与证明和问答联动。
For let the number A by multiplying the two numbers B, C make D, E; I say that, as B is to C, so is D to E. For, since A by multiplying B has made D, therefore B measures D according to the units in A.
设数A乘以数B和C分别得D和E。
But the unit F also measures the number A according to the units in it; therefore the unit F measures the number A the same number of times that B measures D.
因为A乘以B得D，所以B以A中的单位数度量D。
Therefore, as the unit F is to the number A, so is B to D.
单位F以自身中的单位数度量A，因此F度量A的次数等于B度量D的次数，故单位F比A等于B比D。
[VII. Def. 20] For the same reason, as the unit F is to the number A, so also is C to E; therefore also, as B is to D, so is C to E.
同理，单位F比A等于C比E，因此B比D等于C比E，即B比C等于D比E。