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
 The ancient Greeks knew of four perfect numbers: 6, 28, 496, and 8128, which correspond to $n= 2$, 3, 5, and 7, respectively.
Modern Formulation
See even perfect numbers.
Table of Contents
Proofs: 1
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Propositions: 1
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References
Adapted from (subject to copyright, with kind permission)
 Fitzpatrick, Richard: Euclid's "Elements of Geometry"
Adapted from CC BYSA 3.0 Sources:
 Prime.mover and others: "Pr∞fWiki", https://proofwiki.org/wiki/Main_Page, 2016