For, if possible, let it be so.
Now A, B, C measure DE;
therefore G also will measure DE.
But it also measures EF.
Therefore G, being a number, will measure the remainder, the unit DF: which is absurd.
Therefore G is not the same with any one of the numbers A, B, C.
And by hypothesis it is prime.
Therefore the prime numbers A, B, C, G have been found which are more than the assigned multitude of A, B, C.
Q. E. D.