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.
Euclid. Euclid's Elements. Sir Thomas Little Heath. New York. Dover. 1956.
The National Science Foundation provided support for entering this text.
Purchase a copy of this text (not necessarily the same edition) from
An XML version of this text is available for download,
with the additional restriction that you offer Perseus any modifications you make. Perseus provides credit for all accepted
changes, storing new additions in a versioning system.