Proof: By Euclid
(related to Proposition: 8.07: First Element of Geometric Progression that divides Last also divides Second)
- For if $A$ does not measure $B$ (in a geometric progression $A$, $B$, $C$, $D$), then no other (number) will measure any other (number) either [Prop. 8.6].
- But $A$ measures $D$.
- Thus, $A$ also measures $B$.
- (Which is) the very thing it was required to show.
Adapted from (subject to copyright, with kind permission)
- Fitzpatrick, Richard: Euclid's "Elements of Geometry"