\begin{definition}[Definition:Side of Sum of Medial Areas]
Let $a, b \in \R_{>0}$ be in the forms:
:$a = \dfrac {\rho \lambda^{1/4} } {\sqrt 2} \sqrt {1 + \dfrac k {\sqrt {1 + k^2} } }$
:$b = \dfrac {\rho \lambda^{1/4} } {\sqrt 2} \sqrt {1 - \dfrac k {\sqrt {1 + k^2} } }$
where:
: $\rho$ is a rational number
: $k$ is a rational number whose square root is irrational
: $\lambda$ is a rational number whose square root is irrational.
Then $a + b$ is the '''side of the sum of (two) medial areas'''.
{{:Euclid:Proposition/X/41}}
\end{definition}