PROPOSITION 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, AB, BC, CD, DE, be added together ;

I say that the whole AE is even.

A B C D E
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.

Dependency Graph

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Required for

IX.22, IX.23, IX.28, IX.29, IX.30, IX.31

See Commentary on Proposition IX.21.