Definition:Bimedial/Second Bimedial
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Definition
Let $a, b \in \R_{>0}$ be in the forms:
- $a = k^{1/4} \rho$
- $b = \dfrac {\lambda^{1/2} \rho} {k^{1/4} }$
where:
- $\rho$ is a rational number
- $k$ is a rational number whose square root is irrational.
- $\lambda$ is a rational number whose square root is irrational.
Then $a + b$ is a second bimedial.
In the words of Euclid:
- If two medial straight lines commensurable in square only and containing a medial rectangle be added together, the whole is irrational; and let it be called a second bimedial straight line.
(The Elements: Book $\text{X}$: Proposition $38$)