If from an even number an even number be subtracted, the remainder will be even.
For from the even number AB let the even number BC be subtracted:
I say that the remainder CA is even.
For, since AB is even, it has a half part. [VII. Def. 6]
For the same reason BC also has a half part;
so that the remainder [CA also has a half part, and] AC is therefore even.
Q. E. D.