Proof: By Euclid
(related to Proposition: Prop. 9.21: Sum of Even Numbers is Even)
 For let any multitude whatsoever of even numbers, $AB$, $BC$, $CD$, $DE$, lie together.
 I say that the whole, $AE$, is even.
 For since everyone of $AB$, $BC$, $CD$, $DE$ is even, it has a half part [Def. 7.6] .
 And hence the whole $AE$ has a half part.
 And an even number is one (which can be) divided in half [Def. 7.6] .
 Thus, $AE$ is even.
 (Which is) the very thing it was required to show.
∎
Thank you to the contributors under CC BYSA 4.0!
 Github:

 nonGithub:
 @Fitzpatrick
References
Adapted from (subject to copyright, with kind permission)
 Fitzpatrick, Richard: Euclid's "Elements of Geometry"