Proposition: Prop. 10.093: Side of Area Contained by Rational Straight Line and Third Apotome

(Proposition 93 from Book 10 of Euclid's “Elements”)

If an area is contained by a rational (straight line) and a third apotome then the square root of the area is a second apotome of a medial (straight line). * For let the area $AB$ have been contained by the rational (straight line) $AC$ and the third apotome $AD$. * I say that the square root of area $AB$ is the second apotome of a medial (straight line).


Modern Formulation

(not yet contributed)

Proofs: 1

Proofs: 1

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