| 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. | VIII.21 | |
| Therefore, if four numbers are in continued proportion, and the first is a cube, then the fourth is also a cube. | ||
| Q.E.D. | ||
Book VIII Introduction - Proposition VIII.22 - Proposition VIII.24.