For, if not, A is either equal to B or less.
Now A is not equal to B;
for in that case each of the magnitudes A, B would have had the same ratio to C; [V. 7]
but they have not; therefore A is not equal to B.
Nor again is A less than B;
for in that case A would have had to C a less ratio than B has to C; [V. 8]
but it has not; therefore A is not less than B.
But it was proved not to be equal either;
therefore A is greater than B.
Complete text
Book I