If from an odd number an odd number be subtracted, the remainder will be even.
For from the odd number AB let the odd number BC be subtracted;
I say that the remainder CA is even.
For, since AB is odd, let the unit BD be subtracted;
therefore the remainder AD is even. [VII. Def. 7]
For the same reason CD is also even; [VII. Def. 7]
so that the remainder CA is also even. [IX. 24]
Q. E. D.