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Proposition: Prop. 10.099: Square on Second Apotome of Medial Straight Line applied to Rational Straight Line

(Proposition 99 from Book 10 of Euclid's “Elements”)

The (square) on a second apotome of a medial (straight line), applied to a rational (straight line), produces a third apotome as breadth.

• Let $AB$ be the second apotome of a medial (straight line), 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 third 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