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Proposition: Prop. 10.062: Square on Second Bimedial Straight Line applied to Rational Straight Line

(Proposition 62 from Book 10 of Euclid's “Elements”)

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

• Let $AB$ be a second bimedial (straight line) having been divided into its (component) medial (straight lines) at $C$, such that $AC$ is the greater segment.
• And let $DE$ be some rational (straight line).
• 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 third 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