Elements of Geometric Sequence from One which Divide Later Elements/Porism
Jump to navigation
Jump to search
Porism to Elements of Geometric Sequence from One which Divide Later Elements
In the words of Euclid:
- And it is manifest that, whatever place the measuring number has, reckoned from the unit, the same place also has the number according to which it measures, reckoned from the number measured, in the direction of the number before it.
(The Elements: Book $\text{IX}$: Proposition $11$ : Porism)
Proof
Apparent from the construction.
$\blacksquare$
Historical Note
This proof is Proposition $11$ of Book $\text{IX}$ 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 $\text{IX}$. Propositions