If as many even numbers as we please be added together, the whole is even.
For let as many even numbers as we please, AB, BC, CD, DE, be added together;
I say that the whole AE is even.
For, since each of the numbers AB, BC, CD, DE is even, it has a half part; [VII. Def. 6]
so that the whole AE also has a half part.
But an even number is that which is divisible into two equal parts; [id.]
therefore AE is even.
Q. E. D.