If a cube number by multiplying a cube number make some number, the product will be cube.
若一立方数乘以另一立方数得某数，则其积为立方数。
立方数 A、B 与它们的积 C = A·B；D = A·A 也是立方数。A:B = D:C；A、B 间有两项比例中项，故 D、C 间也有，C 为立方数。
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For let the cube number A by multiplying the cube number B make C; I say that C is cube. For let A by multiplying itself make D; therefore D is cube.
设立方数A乘以立方数B得C，则C为立方数。
[IX. 3] And, since A by multiplying itself has made D, and by multiplying B has made C therefore, as A is to B, so is D to C.
令A自乘得D，由第九卷命题3知D为立方数。
[VII. 17] And, since A, B are cube numbers, A, B are similar solid numbers.
因A自乘得D，且A乘B得C，故A比B等于D比C（第七卷命题17）。
Therefore two mean proportional numbers fall between A, B; [VIII. 19] so that two mean proportional numbers will fall between D, C also.
因A、B均为立方数，故为相似立体数，其间有两个比例中项（第八卷命题19），从而D与C间亦有两个比例中项（第八卷命题8），故C为立方数。