Perspective Polygons

Extract

Desargues’ theorem is concerned with two triangles in perspective for some point O. Let us denote the vertices of the first triangle by , it is then natural to denote the sides by where is the side containing . Now bringing in the second triangle we get sides . Moreover, one pair of corresponding sides is ; it is therefore natural to christen their intersection . The other two meets are ; and, by Desargues' theorem, these three meets are collinear; we therefore christen the axis of perspective .