Commentary on Proposition IV.12

Back to Proposition IV.12.

[Folio 0110 | p. 104]

De Morgan remarks that IV. 12, 13, 14 supply the place of the following: Having given a regular polygon of any number of sides inscribed in a circle, to describe the same about the circle; and, having given the polygon, to inscribe and circumscribe a circle. For the method can be applied generally, as indeed Euclid practically says in the Porism to IV. 15 about the regular hexagon and in the remark appended to IV. 16 about the regular fifteen-angled figure.

The conclusion of this proposition, “therefore about the given circle an equilateral and equiangular pentagon has been circumscribed,” is omitted in the MSS.