If as many even numbers as we please are added together, then the sum is even. | ||
Let as many even numbers as we please, AB, BC, CD, and DE, be added together.
I say that the sum AE is even. |
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Since each of the numbers AB, BC, CD, and DE is even, therefore each has a half part, so that the sum AE also has a half part. But an even number is that which is divisible into two equal parts, therefore AE is even. | VII.Def.6 | |
Therefore, if as many even numbers as we please are added together, then the sum is even. | ||
Q.E.D. |
Book IX Introduction - Proposition IX.20 - Proposition IX.22.