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

(not yet contributed)

Proofs: 1 Corollaries: 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