\begin{definition}[Definition:Binomial (Euclidean)/Fifth Binomial]
Let $a$ and $b$ be two (strictly) positive real numbers such that $a + b$ is a binomial.
Then $a + b$ is a '''fifth binomial''' {{iff}}:
: $(1): \quad b \in \Q$
: $(2): \quad \dfrac {\sqrt {a^2 - b^2}} a \notin \Q$
where $\Q$ denotes the set of rational numbers.
{{EuclidSaid}}
:''{{Definition:Euclid's Definitions - Book X (II)/5 - Fifth Binomial}}''
{{EuclidDefRefNocat|X (II)|5|Fifth Binomial}}
\end{definition}