Editing Desargues's theorem (section)

==The Desargues configuration==
{{main|Desargues configuration}}
[[Image:Mutually-inscribed-pentagons.svg|thumb|The Desargues configuration viewed as a pair of mutually inscribed pentagons: each pentagon vertex lies on the line through one of the sides of the other pentagon.]]
The ten lines involved in Desargues's theorem (six sides of triangles, the three lines {{math|{{overline|''Aa''}}, {{overline|''Bb''}}}} and {{math|{{overline|''Cc''}}}}, and the axis of perspectivity) and the ten points involved (the six vertices, the three points of intersection on the axis of perspectivity, and the center of perspectivity) are so arranged that each of the ten lines passes through three of the ten points, and each of the ten points lies on three of the ten lines. Those ten points and ten lines make up the [[Desargues configuration]], an example of a [[projective configuration]]. Although Desargues's theorem chooses different roles for these ten lines and points, the Desargues configuration itself is more [[symmetry|symmetric]]: ''any'' of the ten points may be chosen to be the center of perspectivity, and that choice determines which six points will be the vertices of triangles and which line will be the axis of perspectivity.