# 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)