DESARGRES, G.(1591-ca.1662)

In 1639, nine years after kepler's death, there appeared in Paris a remarkably original but little -heeded treatise on the conic sections. It was written by Gerard Desargues, an engineer, architectm and one-time French army officer, who was born in Lyons in 1591 and who died in the same city about 1662. The work was so generally neglected by other mathematicians that it was soon forgotten, and all copies of the publication

disappeared.  Two centuries later, when the French geometer Michel Chasles(1793-1880) wrote his still-valuable history of geometry, there was no means of estimating the valus of Desargues'work.   Six years later, howeve, in 1845, Chasles happened upon a manyscript copy of the treatise, made by Desargues pupil.   Philippe de la Hire (1640-1718); since that time, the work has been regarded as one of the classics in the early development of synthetic projective geometry.
    Serveral reasons can be advanced to accont for the initial neglect of Desargues' little volume.  It was overahadowed by the more supple analytic geometry introduced by Descartes two years earlier. Geometers were generally expending their energie either developing this new powerful tool or trying to apply infinitesimals to geometry.  Also, Desargues adopted an unfortunate and eccentric style of writing.  He introdrced some seventy new terms, many of a recondite botanical origin, of which only one, involution, has survived.  Curiously enough, involution was preserved because it was the one piece of Desargues' technical jargon that was singled out for the sharpest criticism and ridicule by his reviewer.
    Desargues wrote other books besides the one on conic sections, one of them being a treatise on how to teach children to sing well.  But it is the little Book on conic sections that marks him as the most original contributor to synthetic geometry in the seventeenth century.  Starting with Kepler's doctrine of continuity, the work develops many of the fundamental theorems on invelution, harmonic ranges, homology, poles and polars, and perspective-topics familiar to those who have taken one of our present-day courses in prejective geometry.  One interedting concept is that the notion of poles and polars may be extended to apheres and to certain other surfaces of the second degree.  It is likely that Desargues was aware of only a few of the surfaces of second degree, many of these surfaces probably remaining unknown until their complete enumeration by Euler in 1748. Elsewhere we find Desargues' fundamental two-triangle theorem:If two triangles, inthe same plane or not, are sosituated that lines joining pairs of corresponding vertices are concurrent, then the points of interesection of pairs of corresponding sides are collinear, and conversely.

Desargues, when he was in his thirties and living in Paris, made a considerable impression on his contemporarices through a series of gratuitouw lectres. His work was appreciated by Descartes, and blaise Pascal once credited Desargues as being the source of much of his inspiration. La Hire, with considerable labor, tried to show that all the theorems of Apollonius' Conic Sections can be derived from the circle by Desargues' method of central projection. In spote of all this, however, the new geometry took little hold in the seventeenth centry, and the subhect lay practically domant until the early part of the nineteenth century, when enormous interest in the subject developed and great advances were made by such man as Gergonne, Poncelet, Brianchon, Dupin, Chasles, and Steiner. Whereas Desargues may have been motivated by the need of a theory of perspective for architects and draftsmen, these later writers developed the subject for its own intrinsic charm.