Proposition: 9.36: Theorem of Even Perfect Numbers (First Part)

Euclid's Formulation

If any multitude whatsoever of numbers is set out continuously in a double proportion, (starting) from a unit, until the whole sum added together becomes prime, and the sum multiplied into the last (number) makes some (number), then the (number so) created will be perfect. * For let any multitude of numbers, $A$, $B$, $C$, $D$, be set out (continuouly) in a double proportion, until the whole sum added together is made prime.


Historical Notes

Modern Formulation

See even perfect numbers.

Proofs: 1

Propositions: 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