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Proposition: Prop. 10.101: Square on Straight Line which produces Medial Whole with Rational Area applied to Rational Straight Line

(Proposition 101 from Book 10 of Euclid's “Elements”)

The (square) on that (straight line) which with a rational (area) makes a medial whole, applied to a rational (straight line), produces a fifth apotome as breadth.

• Let $AB$ be that (straight line) which with a rational (area) makes a medial whole, and $CD$ a rational (straight line).
• And let $CE$, equal to the (square) on $AB$, have been applied to $CD$, producing $CF$ as breadth.
• I say that $CF$ is a fifth apotome.

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