第8卷命题 27 · 相似体数之比为立方数比

Let A, B be similar solid numbers; I say that A has to B the ratio which a cube number has to a cube number.

设A、B为相似体数，则A与B之间有两个比例中项C、D。

For, since A, B are similar solid numbers, therefore two mean proportional numbers fall between A, B.

取与A、C、D、B同比例且个数相等的最小数组E、F、G、H。

[VIII. 19] Let C, D so fall, and let E, F, G, H, the least numbers of those which have the same ratio with A, C, D, B, and equal with them in multitude, be taken; [VII. 33 or VIII. 2] therefore the extremes of them E, H are cube.

根据第八卷命题2的推论，E和H是立方数。

因此A与B的比等于立方数E与立方数H的比。