Proposition: Prop. 13.05: Straight Line cut in Extreme and Mean Ratio plus its Greater Segment

(Proposition 5 from Book 13 of Euclid's “Elements”)

If a straight line is cut in extreme and mean ratio, and a (straight line) equal to the greater piece is added to it, then the whole straight line has been cut in extreme and mean ratio, and the original straight line is the greater piece.


Modern Formulation

(not yet contributed)

Proofs: 1

Proofs: 1

Thank you to the contributors under CC BY-SA 4.0!



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