Proof: By Euclid
(related to Proposition: Prop. 9.29: Odd Number multiplied by Odd Number is Odd)
 For since $A$ has made $C$ (by) multiplying $B$, $C$ is thus composed out of so many (magnitudes) equal to $B$, as many as (there) are units in $A$ [Def. 7.15] .
 And each of $A$, $B$ is odd.
 Thus, $C$ is composed out of odd (numbers), (and) the multitude of them is odd.
 Hence $C$ is odd [Prop. 9.23].
 (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"