Definition:Apotome

Definition
Let $a, b \in \R_{>0}$ be (strictly) positive real numbers.

Then $a - b$ is an apotome iff:
 * $\displaystyle \frac a b \not \in \Q$ and $\displaystyle \left({\frac a b}\right)^2 \in \Q$ and $a - b \not \in \Q$ and $a - b > 0$.

$a$ is called the whole and $b$ is called the annex.


 * If a rational straight line, which is commensurable in square only with the whole, is subtracted from another rational straight line, and the remainder is an irrational straight line, let this be called an apotome.

(: Book X: Proposition $73$)

Linguistic Note
The term apotome is archaic, and is rarely used nowadays.

It is pronounced a-pot-o-mee.