Proposition: Prop. 8.20: Numbers between which exists one Mean Proportional are Similar Plane
(Proposition 20 from Book 8 of Euclid's “Elements”)
If one number falls between two numbers in mean proportion then the numbers will be similar plane (numbers) .
* For let one number $C$ fall between the two numbers $A$ and $B$ in mean proportion.
* I say that $A$ and $B$ are similar plane numbers.
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Table of Contents
Proofs: 1 2 3
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