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) .
* Let $AB$ be a rational (area), and $CD$ a medial (area) .
* I say that the square root of area $AD$ is either binomial, or first bimedial, or major, or the square root of a rational plus a medial (area) .
Modern Formulation
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Table of Contents
Proofs: 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