Proposition: Prop. 8.21: Numbers between which exist two Mean Proportionals are Similar Solid

(Proposition 21 from Book 8 of Euclid's “Elements”)

If two numbers fall between two numbers in mean proportion then the (latter) are similar solid (numbers) . * For let the two numbers $C$ and $D$ fall between the two numbers $A$ and $B$ in mean proportion. * I say that $A$ and $B$ are similar solid (numbers) . fig21e

Modern Formulation

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Proofs: 1

Proofs: 1

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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