Second Bimedial is Irrational/Mistake
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Source Work
1926: Sir Thomas L. Heath: Euclid: The Thirteen Books of The Elements: Volume 3 (2nd ed.)
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 $38$)
The mistake can be seen in the edition as published by Dover: ISBN 0-486-60089-0.
Mistake
- For let a rational straight line $DE$ be set out, and let the parallelogram $DF$ equal to the square on $AC$ be applied to $DE$, producing $DG$ as breadth. [I.44]
The reference is incorrect.
is not the result needed here.
The correct reference should be: