◀ ▲ ▶Branches / Geometry / Elements-euclid / Book-10-incommensurable-magnitudes / Proposition: Prop. 10.060: Square on Binomial Straight Line applied to Rational Straight Line

Proposition: Prop. 10.060: Square on Binomial Straight Line applied to Rational Straight Line

(Proposition 60 from Book 10 of Euclid's “Elements”)

The square on a binomial (straight line) applied to a rational (straight line) produces as breadth a first binomial (straight line).¹

• Let $AB$ be a binomial (straight line), having been divided into its (component) terms at $C$, such that $AC$ is the greater term.
• And let the rational (straight line) $DE$ be laid down.
• And let the (rectangle) $DEFG$, equal to the (square) on $AB$, have been applied to $DE$, producing $DG$ as breadth.
• I say that $DG$ is a first binomial (straight line).

Modern Formulation

(not yet contributed)

Table of Contents

Proofs: 1

Mentioned in:

Proofs: 1 2

Thank you to the contributors under CC BY-SA 4.0!

Github:

non-Github:

@Fitzpatrick

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