Proof: By Euclid
(related to Proposition: Prop. 9.32: Power of Two is EvenTimes Even Only)
 For let any multitude of numbers whatsoever, $B$, $C$, $D$, have been (continually) doubled, (starting) from the dyad $A$.
 I say that $B$, $C$, $D$ are eventimeseven (numbers) only.
 In fact, (it is) clear that each [of $B$, $C$, $D$] is an eventimeseven (number).
 For it is doubled from a dyad [Def. 7.8] .
 I also say that (they are eventimeseven numbers) only.
 For let a unit be laid down.
 Therefore, since any multitude of numbers whatsoever are in continued proportion, starting from a unit, and the (number) $A$ after the unit is prime, the greatest of $A$, $B$, $C$, $D$, (namely) $D$, will not be measured by any other (numbers) except $A$, $B$, $C$ [Prop. 9.13].
 And each of $A$, $B$, $C$ is even.
 Thus, $D$ is an eventimeseven (number) only [Def. 7.8] .
 So, similarly, we can show that each of $B$, $C$ is [also] an eventimeseven (number) only.
 (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"