# 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: