Definition:Medial Area

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A medial area is an area which is equal to the square on a medial straight line.

Thus an area $A$ is medial if and only if it is of the form:

$A = \rho^2 \sqrt k$


$\rho$ is a rational number
$k$ is a rational number whose square root is irrational.

In the words of Euclid:

From this it is manifest that an area commensurable with a medial area is medial.

(The Elements: Book $\text{X}$: Proposition $23$ : Porism)

Also see