Definition:Bimedial/First Bimedial

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Let $a, b \in \R_{>0}$ be in the forms:

$a = k^{1/4} \rho$
$b = k^{3/4} \rho$


$\rho$ is a rational number
$k$ is a rational number whose square root is irrational.

Then $a + b$ is a first bimedial.

In the words of Euclid:

If two medial straight lines commensurable in square only and containing a rational rectangle be added together, the whole is irrational; and let it be called a first bimedial straight line.

(The Elements: Book $\text{X}$: Proposition $37$)

Also see