Proposition: Prop. 8.20: Numbers between which exists one Mean Proportional are Similar Plane

(Proposition 20 from Book 8 of Euclid's “Elements”)

If one number falls between two numbers in mean proportion then the numbers will be similar plane (numbers) .

Modern Formulation

(not yet contributed)

Proofs: 1

Proofs: 1 2 3

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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",, 2016