| Any number is either prime or is measured by some prime number. | ||
| Let A be a number.
I say that A either is prime or is measured by some A prime number. |
||
| If now A is prime, then that which was proposed is done. | ||
| But if it is composite, then some prime number measures it. | VII.31 | |
| Therefore any number either is prime or is measured by some prime number. | ||
| Therefore, any number is either prime or is measured by some prime number. | ||
| Q.E.D. | ||
Book VII Introduction - Proposition VII.31 - Proposition VII.33.