Similar plane numbers have to one another the ratio which a square number has to a square number.
相似面数之比等于一个平方数比另一个平方数。
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Let A, B be similar plane numbers; I say that A has to B the ratio which a square number has to a square number.
设A、B为相似面数，则根据VIII.18，A与B之间有一个比例中项数C。
For, since A, B are similar plane numbers, therefore one mean proportional number falls between A, B.
取与A、C、B同比的最小数组D、E、F（根据VII.33或VIII.2）。
[VIII. 18] Let it so fall, and let it be C; and let D, E, F, the least numbers of those which have the same ratio with A, C, B, be taken; [VII. 33 or VIII. 2] therefore the extremes of them D, F are square.
因此，根据VIII.2的推论，两端数D和F都是平方数。
由于A比B等于D比F，而D和F是平方数，故A与B之比等于平方数之比。