Elements of Geometric Sequence from One which Divide Later Elements/Porism

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.

Proof

Apparent from the construction.

$\blacksquare$

Historical Note

This proof is Proposition $11$ of Book $\text{IX}$ of Euclid's The Elements.