Definition:Bimedial/First Bimedial

Definition

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

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

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

where:

$\rho$ 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

• Construction of Components of First Bimedial

• First Bimedial is Irrational

• Definition:Second Bimedial