Proposition: Prop. 10.026: Medial Area not greater than Medial Area by Rational Area
(Proposition 26 from Book 10 of Euclid's “Elements”)
A medial (area) does not exceed a medial (area) by a rational (area).
Modern Formulation
In other words, a positive rational number \(\delta\) is never a difference of square roots of two other positive rational numbers $\alpha$ and $\beta$, formally \[\sqrt{\alpha}\sqrt{\beta}\neq \delta\]
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