Proposition: Prop. 8.22: If First of Three Numbers in Geometric Progression is Square then Third is Square
(Proposition 22 from Book 8 of Euclid's “Elements”)
If three numbers are in continued proportion, and the first is square, then the third will also be square.
* Let $A$, $B$, $C$ be three numbers in continued proportion, and let the first $A$ be square.
* I say that the third $C$ is also square.
Modern Formulation
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Table of Contents
Proofs: 1
Mentioned in:
Proofs: 1 2 3 4
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References
Adapted from (subject to copyright, with kind permission)
 Fitzpatrick, Richard: Euclid's "Elements of Geometry"
Adapted from CC BYSA 3.0 Sources:
 Prime.mover and others: "Pr∞fWiki", https://proofwiki.org/wiki/Main_Page, 2016