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
Mentioned in:
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