Area contained by Apotome and Binomial Straight Line Commensurable with Terms of Apotome and in same Ratio/Porism

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Theorem

In the words of Euclid:

And it is made manifest to us by this also that it is possible for a rational area to be contained by irrational straight lines.

(The Elements: Book $\text{X}$: Proposition $114$ : Porism)


Proof

Directly apparent from the construction.

$\blacksquare$


Historical Note

This proof is Proposition $114$ of Book $\text{X}$ of Euclid's The Elements.


Sources