Desargues, Girard (1591–1661)
Girard Desargues was a French mathematician who is regarded as the chief founder of perspective
geometry. His 12-page treatise La perspective (636) consists of a
single worked example in which Desargues sets out a method for constructing
a perspective image without using any point lying outside the picture field.
He considers the representation in the picture of plane of lines that meet
at a point and also of lines that are parallel to each another. In the last
paragraph of the work he considers the problem of finding the perspective
image of a conic section. Three years later,
he wrote his treatise on projective geometry Brouillon project d'une
atteinte aux evenemens des rencontres du cone avec un plan. The first
part of this deals with the properties of sets of straight lines meeting
at a point and of ranges of points lying on a straight line. In the second
part, the properties of conics are investigated in terms of properties of
ranges of points on straight lines and the modern term "point at infinity"
appears for the first time. Desargues shows that he has completely grasped
the connection between conics and perspective; in fact he treats the fact
that any conic can be projected into any other conic as obvious. Given such
innovative work it may seem surprising that the subject didn't develop rapidly
in the following years. That it didn't may be partly due to mathematicians
failing to recognize the power of what had been put forward. On the other
hand the algebraic approach to geometry put forward by René Descartes at almost exactly the same time (1637) may have diverted attention from
Desargue's' projective methods.