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Proposition: Prop. 10.115: From Medial Straight Line arises Infinite Number of Irrational Straight Lines

(Proposition 115 from Book 10 of Euclid's “Elements”)

An infinite (series) of irrational (straight lines) can be created from a medial (straight line), and none of them is the same as any of the preceding (straight lines).

• Let $A$ be a medial (straight line).
• I say that an infinite (series) of irrational (straight lines) can be created from $A$, and that none of them is the same as any of the preceding (straight lines).

Modern Formulation

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Table of Contents

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