Any prime number is prime to any number which it does not measure.
be a prime number, and let it not measure B
; I say that B
are prime to one another.
For, if B
are not prime to one another, some number will measure them.
, and A
does not measure B
, therefore C
is not the same with A
Now, since C
, 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
are prime to one another. Q. E. D.