\begin{definition}[Definition:Major (Euclidean)]
Let $a, b \in \R_{>0}$ in the forms:
:$a = \dfrac \rho {\sqrt 2} \sqrt {1 + \dfrac k {\sqrt {1 + k^2} } }$
:$b = \dfrac \rho {\sqrt 2} \sqrt {1 - \dfrac k {\sqrt {1 + k^2} } }$
where:
: $\rho$ is a rational number
: $k$ is a rational number whose square root is irrational.
Then $a + b$ is a '''major'''.
{{:Euclid:Proposition/X/39}}
\end{definition}