For, since C, D are cube, C, D are similar solid numbers.
Therefore two mean proportional numbers fall between C, D. [VIII. 19]
And, as many numbers as fall between C, D in continued proportion, so many will also fall between those which have the same ratio with them; [VIII. 8]
so that two mean proportional numbers fall between A, B also.
Let E, F so fall.
Since, then, the four numbers A, E, F, B are in continued proportion, and A is cube, therefore B is also cube. [VIII. 23]
Q. E. D.