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 \[\sqrt{\alpha}-\sqrt{\beta}\neq \delta\]

Proofs: 1

Proofs: 1 2 3 4 5 6 7 8

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