| If there are as many numbers as we please in continued proportion, and the first measures the last, then it also measures the second. | ||
| Let there be as many numbers as we please, A, B, C, and D, in continued proportion, and let A measure D.
I say that A also measures B. | ||
| If A does not measure B, neither does any other of the numbers measure any other. But A measures D. Therefore A also measures B. | VIII.6 | |
| Therefore, if there are as many numbers as we please in continued proportion, and the first measures the last, then it also measures the second. | ||
| Q.E.D. | ||
Book VIII Introduction - Proposition VIII.6 - Proposition VIII.8.