\begin{definition}[Definition:Commensurable in Square Only]
Let $a, b \in \R_{>0}$ be (strictly) positive real numbers.
Then $a$ and $b$ are '''commensurable in square only''' {{iff}}:
: $\paren {\dfrac a b}^2$ is rational.
but:
: $\dfrac a b$ is irrational.
That is, such that:
: $a$ and $b$ are commensurable in square
but:
: $a$ and $b$ are incommensurable in length.
{{EuclidSaid}}
:''{{Definition:Euclid's Definitions - Book X/2 - Commensurable in Square}}''
{{EuclidDefRefNocat|X|2|Commensurable in Square}}
and:
:''{{Definition:Euclid's Definitions - Book X/1 - Commensurable}}''
{{EuclidDefRefNocat|X|1|Commensurable}}
\end{definition}