Proof: By Euclid
(related to Proposition: Prop. 9.27: Odd Number minus Even Number is Odd)
 For let the unit $AD$ have been subtracted (from $AB$).
 $DB$ is thus even [Def. 7.7] .
 And $BC$ is also even.
 Thus, the remainder $CD$ is also even [Prop. 9.24].
 $CA$ (is) thus odd [Def. 7.7] .
 (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"