For, since A, B are similar plane numbers, therefore one mean proportional number falls between A, B. [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. [VIII. 2, Por.]
And since, as D is to F, so is A to B, and D, F are square,
therefore A has to B the ratio which a square number has to a square number.
Q. E. D.