\begin{definition}[Definition:Medial]
A '''medial''' is a strictly positive real number which is the mean proportional between two rational line segments which are commensurable in square only.
Thus a magnitude $a \in \R_{>0}$ is '''medial''' {{iff}} $a$ is of the form:
:$a = \rho \sqrt [4] k$
where:
: $\rho$ is a rational number
: $k$ is a rational number whose square root is irrational.
{{:Euclid:Proposition/X/21}}
\end{definition}