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Any prime number is prime to any number which it does not measure.

Let A be a prime number, and let it not measure B; I say that B, A are prime to one another.

For, if B, A are not prime to one another, some number will measure them.

Let C measure them.

Since C measures B, and A does not measure B, therefore C is not the same with A.

Now, since C measures B, A, therefore it also measures A which is prime, though it is not the same with it: which is impossible.

Therefore no number will measure B, A.

Therefore A, B are prime to one another. Q. E. D.

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