For let A by multiplying itself make D;
therefore D is cube. [IX. 3]
Now, since A by multiplying itself has made D, and by multiplying B has made C,
therefore, as A is to B, so is D to C. [VII. 17]
And since D, C are cube, they are similar solid numbers.
Therefore two mean proportional numbers fall between D, C. [VIII. 19]
And, as D is to C, so is A to B;
therefore two mean proportional numbers fall between A, B also. [VIII. 8]
And A is cube;
therefore B is also cube. [VIII. 23]