Branches History Index

◀ ▲ ▶Branches / Geometry / Euclidean-geometry / Elements-euclid / Book-13-platonic-solids / Proposition: Prop. 13.06: Segments of Rational Straight Line cut in Extreme and Mean Ratio are Apotome

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. fig06e

Modern Formulation

(not yet contributed)

Table of Contents

Proofs: 1

Mentioned in:

Proofs: 1

Thank you to the contributors under CC BY-SA 4.0!

Github:
bookofproofs
non-Github:
@Fitzpatrick

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