Proof: By Euclid
(related to Proposition: Prop. 9.26: Odd Number minus Odd Number is Even)
 For since $AB$ is odd, let the unit $BD$ have been subtracted (from it).
 Thus, the remainder $AD$ is even [Def. 7.7] .
 So, for the same (reasons), $CD$ is also even.
 And hence the remainder $CA$ is even [Prop. 9.24].
 (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"