Proof: By Euclid
(related to Lemma: Lem. 10.016: Incommensurability of Sum of Incommensurable Magnitudes)
![fig016ae](https://github.com/bookofproofs/bookofproofs.github.io/blob/main/_sources/_assets/images/euclid/Book10/fig016ae.png?raw=true)
- And it is immediately obvious.
- For since $DB$ is a square, $DC$ is equal to $CB$.
- And $AD$ is the (rectangle contained) by $AC$ and $CD$ - that is to say, by $AC$ and $CB$.
- Thus, if ... to some straight line, and so on ....
∎
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References
Adapted from (subject to copyright, with kind permission)
- Fitzpatrick, Richard: Euclid's "Elements of Geometry"