Girard Desargues

"Parallel lines have a common end point at an infinite distance."

"He who shall wish to disentangle this proposition will easily be able to compose a volume."

"Desargues the architect was doubtless influenced by what in his day was surrealism. In any event, he composed more like an artist than a geometer, inventing the most outrageous technical jargon in mathematics for the enlightenment of himself and the mystification of his disciples. Fortunately Desarguesian has long been a dead language."

"I freely confess that I never had taste for study or research either in physics or geometry except in so far as they could serve as a means of arriving at some sort of knowledge of the proximate causes... for the good and convenience of life, in maintaining health, in the practice of some art,... having observed that a good part of the arts is based on geometry, among others that cutting of stone in architecture, that of sundials, that of perspective in particular."

"Blaise Pascal... was one of the very few contemporaries who appreciated the worth of Desargues. He says in his Essais pour les coniques, "I wish to acknowledge that I owe the little that I have discovered on this subject to his writings."

"Pascal made grateful acknowlegement to Desargues for his skill in projective geometry."

"Desargues also gives the theory of polar lines. What is called "" in elementary works is as follows: If the vertices of two triangles, situated either in space or in a plane, lie on three lines meeting in a point, then their sides meet in three points lying on a line, and conversely. This theorem has been used since by Brianchon, Sturm, Gergonne, and others. Poncelet made it the basis of his beautiful theory of homological figures."

"We owe to Desargues the theory of involution and of transversals; also the beautiful conception that the two extremities of a straight line may be considered as meeting at infinity, and that parallels differ from other pairs of lines only in having their points of intersection at infinity. He re-invented the and showed its application to the construction of gear teeth, a subject elaborated more fully later by La Hire."

"Pascal greatly admired Desargues results... Pascals and Desargues writings contained some of the fundamental ideas of modern synthetic geometry."

"Nous démontrerons aussi la propriété suivante dont le premier inventeur est M. Desargues, Lyonnois, un des grands esprits de ce temps, et des plus versés aux mathématiques, et entre autres aux coniques, dont les écrits sur cette matière, quoiquen petit nombre, en ont donné un ample témoignage à ceux qui auront voulu en recevoir lintelligence. Je veux bien avouer que je dois le peu que jai trouvé sur cette matière à ses écrits, et que jai tâché dimiter, autant quil ma été possible, sa méthode..."

"In 1639, nine years after Keplers death, there appeared in Paris a remarkably original but little-heeded treatise on the conic sections. ...The work was so generally neglected by other mathematicians that it was soon forgotten and all copies of the publication disappeared. ...in 1845 Chasles happened upon a manuscript copy... made by Desargues pupil, ... and since that time the work has been regarded as one of the classics in the early development of synthetic projective geometry."

"When no point of a line is at a finite distance, the line itself is at an infinite distance."