If a cube number measure a cube number, the side will also measure the side; and, if the side measure the side, the cube will also measure the cube.
如果一个立方数量度另一个立方数，则其边也量度其边；反之，如果边量度边，则立方数量度立方数。
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For let the cube number A measure the cube B, and let C be the side of A and D of B; I say that C measures D. For let C by multiplying itself make E, and let D by multiplying itself make G; further, let C by multiplying D make F, and let C, D by multiplying F make H, K respectively.
设立方数A量度立方数B，C是A的边，D是B的边。
Now it is manifest that E, F, G and A, H, K, B are continuously proportional in the ratio of C to D. [VIII. 11, 12] And, since A, H, K, B are continuously proportional, and A measures B, therefore it also measures H.
令C自乘得E，D自乘得G；又令C乘D得F，再令C、D分别乘F得H、K。
[VIII. 7] And, as A is to H, so is C to D; therefore C also measures D. [VII. Def. 20] Next, let C measure D; I say that A will also measure B.
由VIII.11、12，E、F、G与A、H、K、B成连比例，比例等于C比D。
For, with the same construction, we can prove in a similar manner that A, H, K, B are continuously proportional in the ratio of C to D.
因A、H、K、B成连比例且A量度B，故A量度H（VIII.7）；而A比H等于C比D，故C量度D（VII.定义20）。反之，若C量度D，同理可证A量度B。