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