If a cube number by multiplying itself make some number, the product will be cube.
若一个立方数自乘得到某数，则该乘积也是立方数。
立方数 A 与 A 的边 C；D = C·C；C 乘 D 得 A；A 自乘得 B。单位、C、D、A 成连比例（两项比例中项），故 A、B 间亦有两项比例中项，B 为立方数。
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For let the cube number A by multiplying itself make B; I say that B is cube. For let C, the side of A, be taken, and let C by multiplying itself make D. It is then manifest that C by multiplying D has made A. Now, since C by multiplying itself has made D, therefore C measures D according to the units in itself.
设立方数A自乘得B，取A的边C，C自乘得D，则C乘D得A。
But further the unit also measures C according to the units in it; therefore, as the unit is to C, so is C to D. [VII. Def. 20] Again, since C by multiplying D has made A, therefore D measures A according to the units in C. But the unit also measures C according to the units in it; therefore, as the unit is to C, so is D to A.
因C自乘得D，故C以自身单位量D；又单位以自身单位量C，所以单位比C等于C比D。
But, as the unit is to C, so is C to D; therefore also, as the unit is to C, so is C to D, and D to A. Therefore between the unit and the number A two mean proportional numbers C, D have fallen in continued proportion. Again, since A by multiplying itself has made B, therefore A measures B according to the units in itself.
因C乘D得A，故D以C的单位量A；又单位以C的单位量C，所以单位比C等于D比A。结合前比得单位、C、D、A成连比例。
But the unit also measures A according to the units in it; therefore, as the unit is to A, so is A to B. [VII. Def. 20] But between the unit and A two mean proportional numbers have fallen; therefore two mean proportional numbers will also fall between A, B. [VIII. 8] But, if two mean proportional numbers fall between two numbers, and the first be cube, the second will also be cube.
因A自乘得B，故A以自身单位量B，所以单位比A等于A比B。由单位与A间已有两个中项C、D，据VIII.8知A与B间也有两个中项；又据VIII.23，若两数间有两个中项且第一个为立方，则第二个也为立方，故B为立方。