Proposition: Prop. 10.010: Construction of Incommensurable Lines

(Proposition 10 from Book 10 of Euclid's “Elements”)¹

To find two straight lines incommensurable with a given straight line, the one (incommensurable) in length only, the other also (incommensurable) in square.

Let $A$ be the given straight line.
So it is required to find two straight lines incommensurable with $A$, the one (incommensurable) in length only, the other also (incommensurable) in square.

Modern Formulation

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Proofs: 1

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References

Adapted from (subject to copyright, with kind permission)

Fitzpatrick, Richard: Euclid's "Elements of Geometry"

Adapted from CC BY-SA 3.0 Sources:

Prime.mover and others: "Pr∞fWiki", https://proofwiki.org/wiki/Main_Page, 2016

Footnotes

This whole proposition is regarded by Heiberg as an interpolation into the original text (translator's note). ↩

◀ ▲ ▶Branches / Geometry / Elements-euclid / Book-10-incommensurable-magnitudes / Proposition: Prop. 10.010: Construction of Incommensurable Lines

Proposition: Prop. 10.010: Construction of Incommensurable Lines

(Proposition 10 from Book 10 of Euclid's “Elements”)¹

Modern Formulation

Table of Contents

References

Adapted from (subject to copyright, with kind permission)

Adapted from CC BY-SA 3.0 Sources:

Footnotes

◀ ▲ ▶Branches / Geometry / Elements-euclid / Book-10-incommensurable-magnitudes / Proposition: Prop. 10.010: Construction of Incommensurable Lines

Proposition: Prop. 10.010: Construction of Incommensurable Lines

(Proposition 10 from Book 10 of Euclid's “Elements”)1

Modern Formulation

Table of Contents

References

Adapted from (subject to copyright, with kind permission)

Adapted from CC BY-SA 3.0 Sources:

Footnotes

(Proposition 10 from Book 10 of Euclid's “Elements”)¹