Definition:Bimedial/First Bimedial
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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 $37$)