Proposition: Prop. 13.06: Segments of Rational Straight Line cut in Extreme and Mean Ratio are Apotome
(Proposition 6 from Book 13 of Euclid's “Elements”)
If a rational straight line is cut in extreme and mean ratio then each of the pieces is that irrational (straight line) called an apotome.
* Let $AB$ be a rational straight line cut in extreme and mean ratio at $C$, and let $AC$ be the greater piece.
* I say that $AC$ and $CB$ is each that irrational (straight line) called an apotome.
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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