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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.

Modern Formulation

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Table of Contents

Proofs: 1

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Proofs: 1

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References

Adapted from (subject to copyright, with kind permission)

1. Fitzpatrick, Richard: Euclid's "Elements of Geometry"

Adapted from CC BY-SA 3.0 Sources:

1. Prime.mover and others: "Pr∞fWiki", https://proofwiki.org/wiki/Main_Page, 2016