Proposition 23
If four numbers are in continued proportion, and the first is a cube, then the fourth is also a cube.
Let A, B, C, and D be four numbers in continued proportion, and let A be a cube.
I say that D is also a cube.
Since between A and D there are two mean proportional numbers B and C, therefore A and D are similar solid numbers. But A is a cube, therefore D is also a cube.
Therefore, if four numbers are in continued proportion, and the first is a cube, then the fourth is also a cube.
Q.E.D.