Proposition: Prop. 9.12: Elements of Geometric Progression from One Divisible by Prime

Euclid's Formulation

If any multitude whatsoever of numbers is in continued proportion, (starting) from a unit, then however many prime numbers the last (number) is measured by, the (number) next to the unit will also be measured by the same (prime numbers). * Let any multitude whatsoever of numbers, $A$, $B$, $C$, $D$, be in (continued) proportion, (starting) from a unit. * I say that however many prime numbers $D$ is measured by, $A$ will also be measured by the same (prime numbers).


Modern Formulation

(not yet contributed)

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