| 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. |
||
| 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.