Commentary on Proposition III.22

Back to Proposition III.22.

[Folio 0058 | p. 52]

As Todhunter remarks, the converse of this proposition is true and very important: if two opposite angles of a quadrilateral be together equal to two right angles, a circle may be circumscribed about the quadrilateral. We can, by the method of III. 9, or by IV. 5, circumscribe a circle about the triangle ABC; and we can then prove, by reductio ad absurdum, that the circle passes through the fourth angular point D.