Definition:Medial Area
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Definition
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:
- $A = \rho^2 \sqrt k$
where:
- $\rho$ 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)