Proposition: Prop. 8.23: If First of Four Numbers in Geometric Progression is Cube then Fourth is Cube
(Proposition 23 from Book 8 of Euclid's “Elements”)
If four numbers are in continued proportion, and the first is cube, then the fourth will also be cube.
* Let $A$, $B$, $C$, $D$ be four numbers in continued proportion, and let $A$ be cube.
* I say that $D$ is also cube.
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Table of Contents
Proofs: 1 2 3 4 5 6 7
Adapted from (subject to copyright, with kind permission)
- Fitzpatrick, Richard: Euclid's "Elements of Geometry"
Adapted from CC BY-SA 3.0 Sources:
- Prime.mover and others: "Pr∞fWiki", https://proofwiki.org/wiki/Main_Page, 2016