Euclid:Proposition/IV/16/Corollary

Proposition

In the words of Euclid:

And, in like manner as in the case of the pentagon, if through the points of division on the circle we draw tangents to the circle, there will be circumscribed about the circle a fifteen-angled figure which is equilateral and equiangular.

And further, by proofs similar to those in the case of the regular pentagon, we can both inscribe a circle in the given fifteen-angled figure and circumscribe one about it.

(The Elements: Book $\text{IV}$: Proposition $16$ : Corollary)

Sources

• 1926: Sir Thomas L. Heath: Euclid: The Thirteen Books of The Elements: Volume 2 (2nd ed.) ... (previous) ... (next): Book $\text{IV}$. Propositions