Proposition: Prop. 10.071: Sum of Rational Area and Medial Area gives rise to four Irrational Straight Lines

(Proposition 71 from Book 10 of Euclid's “Elements”)

When a rational and a medial (area) are added together, four irrational (straight lines) arise (as the square root of the total area) - either a binomial, or a first bimedial, or a major, or the square root of a rational plus a medial (area) .


Modern Formulation

(not yet contributed)

Proofs: 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