\begin{definition}[Definition:Apotome/First Apotome]
Let $a, b \in \set {x \in \R_{>0} : x^2 \in \Q}$ be two rationally expressible numbers such that $a - b$ is an apotome.
Then $a - b$ is a '''first apotome''' {{iff}}:
:$(1): \quad a \in \Q$
:$(2): \quad \dfrac {\sqrt {a^2 - b^2}} a \in \Q$
where $\Q$ denotes the set of rational numbers.
{{EuclidSaid}}
:''{{Definition:Euclid's Definitions - Book X (III)/1 - First Apotome}}''
{{EuclidDefRefNocat|X (III)|1|First Apotome}}
\end{definition}