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Proposition: Prop. 13.02: Converse of Area of Square on Greater Segment of Straight Line cut in Extreme and Mean Ratio

(Proposition 2 from Book 13 of Euclid's “Elements”)

If the square on a straight line is five times the (square) on a piece of it, and double the aforementioned piece is cut in extreme and mean ratio, then the greater piece is the remaining part of the original straight line.

• For let the square on the straight line $AB$ be five times the (square) on the piece of it, $AC$.
• And let $CD$ be double $AC$.
• I say that if $CD$ is cut in extreme and mean ratio then the greater piece is $CB$.

Modern Formulation

(not yet contributed)

Table of Contents

Proofs: 1

1. Lemma: Lem. 13.02: Converse of Area of Square on Greater Segment of Straight Line cut in Extreme and Mean Ratio

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References

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", https://proofwiki.org/wiki/Main_Page, 2016