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.