Proof: By Euclid
(related to Proposition: Prop. 9.24: Even Number minus Even Number is Even)
 For since $AB$ is even, it has a half part [Def. 7.6] .
 So, for the same (reasons), $BC$ also has a half part.
 And hence the remainder [$CA$ has a half part].
 Thus, $AC$ is even.
 (Which is) the very thing it was required to show.
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References
Adapted from (subject to copyright, with kind permission)
 Fitzpatrick, Richard: Euclid's "Elements of Geometry"