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Proposition: Prop. 9.11: Elements of Geometric Progression from One which Divide Later Elements

(Proposition 11 from Book 9 of Euclid's “Elements”)

If any multitude whatsoever of numbers is in continued proportion, (starting) from a unit, then a lesser (number) measures a greater according to some existing (number) among the proportional numbers.

• Let any multitude whatsoever of numbers, $B$, $C$, $D$, $E$, be in continued proportion, (starting) from the unit $A$.
• I say that, for $B$, $C$, $D$, $E$, the least (number), $B$, measures $E$ according to some (one) of $C$, $D$.

Modern Formulation

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Table of Contents

Proofs: 1 Corollaries: 1

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Proofs: 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