◀ ▲ ▶Branches / Geometry / Elements-euclid / Book-10-incommensurable-magnitudes / Proposition: Prop. 10.061: Square on First Bimedial Straight Line applied to Rational Straight Line

Proposition: Prop. 10.061: Square on First Bimedial Straight Line applied to Rational Straight Line

(Proposition 61 from Book 10 of Euclid's “Elements”)

The square on a first bimedial (straight line) applied to a rational (straight line) produces as breadth a second binomial (straight line).¹

• Let $AB$ be a first bimedial (straight line) having been divided into its (component) medial (straight lines) at $C$, of which $AC$ (is) the greater.
• And let the rational (straight line) $DE$ be laid down.
• And let the parallelogram $DF$, equal to the (square) on $AB$, have been applied to $DE$, producing $DG$ as breadth.
• I say that $DG$ is a second binomial (straight line).

Modern Formulation

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Table of Contents

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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

Footnotes