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"