Area contained by Apotome and Binomial Straight Line Commensurable with Terms of Apotome and in same Ratio/Porism
Jump to navigation
Jump to search
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
- 1926: Sir Thomas L. Heath: Euclid: The Thirteen Books of The Elements: Volume 3 (2nd ed.) ... (previous) ... (next): Book $\text{X}$. Propositions