The French mathematician Gerard Desargues (1593–1662) was one of the earliest contributors to the study of Projective Geometry. A theorem known as “Desargues theorem” bears his name and often set him as inventor of Projective Geometry. This theorem is very useful in the development of Projective Geometry. It is about relating two aspects of a pair of triangles: pair of three vertices and pair of three sides.
Desarguesian Plane
The Desarguesian plane is a projective plane in which Desargue's triangle theorem holds. The Desargue's triangle theorem is stated as below.
If two triangles are so situated that line joining the pair of corresponding vertices are concurrent then the points of intersection of pair of corresponding sides are collinear and conversely.
This theorem can be
stated as “if two triangles are central couple then they are axial couple and conversely”.
The Desargues theorem can also be stated as “if two triangles are perspective from a point then they are perspective from a line and conversely”.
In the figure below, \( \triangle abc\) and \( \triangle a'b'c'\) satisfy Desargues triangle theorem
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