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. |
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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.