If a number be parts of a number, and another be the same parts of another, alternately also, whatever parts or part the first is of the third, the same parts or the same part will the second also be of the fourth.
如果一个数是另一个数的若干部分，且另一个数是第三个数的相同若干部分，则交替地，第一个数是第三个数的若干部分或一部分，第二个数也是第四个数的相同若干部分或相同一部分。
本页以“第七卷命题10：交替比例保持”整体图解辅助阅读；点、线、角、圆索引已按命题文字和证明步骤校订，可与证明和问答联动。
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 AB be parts of the number C, and another, DE, the same parts of another, F; I say that, alternately also, whatever parts or part AB is of DE, the same parts or the same part is C of F also.
设数AB是数C的若干部分，且数DE是数F的相同若干部分。
For since, whatever parts AB is of C, the same parts also is DE of F, therefore, as many parts of C as there are in AB, so many parts also of F are there in DE.
由于AB是C的若干部分，DE是F的相同若干部分，故AB中所含C的部分数等于DE中所含F的部分数。
Let AB be divided into the parts of C, namely AG, GB, and DE into the parts of F, namely DH, HE; thus the multitude of AG, GB will be equal to the multitude of DH, HE.
将AB按C的部分分为AG、GB，将DE按F的部分分为DH、HE，则AG、GB的个数等于DH、HE的个数。
Now since, whatever part AG is of C, the same part also is DH of F, alternately also, whatever part or parts AG is of DH, the same part or the same parts is C of F also.
由第七卷命题9，AG是C的某一部分，DH是F的相同一部分，故交替地，AG是DH的若干部分或一部分时，C也是F的相同若干部分或相同一部分。