Proposition: Prop. 10.088: Construction of Fourth Apotome

(Proposition 88 from Book 10 of Euclid's “Elements”)

To find a fourth apotome.

fig088e

Modern Formulation

This proposition proves that the fourth apotome has length \[\alpha-\frac \alpha{\sqrt{1+\beta}},\]

where \(\alpha,\beta\) denote positive rational numbers.

Notes

See also [Prop. 10.51].

Proofs: 1

Propositions: 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