G.351 many even numbers — Heath
IX.21
If as many
even numbers as we please be added together, the whole is even.
For let as many even numbers as we please, / A B /, / B C /, / C D /, / D E /, be added together ;
I say that the whole / A E / is even.
For, since each of the
numbers / A B /,
/ B C /,
/ C D /,
/ D E / is even, it has a half part ;
[G.302]so that the whole / A E / also has a half part.
But an even number is that which is divisible into two equal parts ;
[G.302]therefore / A E / is even.
Q. E. D.
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