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Proposition: Prop. 10.103: Straight Line Commensurable with Apotome

Euclid's Formulation

A (straight line) commensurable in length with an apotome is an apotome, and (is) the same in order. * Let $AB$ be an apotome, and let $CD$ be commensurable in length with $AB$. * I say that $CD$ is also an apotome, and (is) the same in order1 as $AB$.

fig103e

Modern Formulation

(not yet contributed)

Table of Contents

Proofs: 1

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non-Github:
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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

  1. Euclid's expression "(not) being the same in order" means that the resulting irrational number is "(not) of the same kind" as that irrational number, with which it is commensurable. ↩