This entry contributed by Margherita Barile

French mathematician, considered as the founder of projective geometry. There seems not to be much reliable information on his life and work, most of what we know comes from indirect sources. Desargues used to write down his ideas in form of brief sketches, none of which was intended for publication, and many of which went lost. He made no effort to make them understandable to potential readers: he used "microscopic characters" (Poudra 1864), an exceedingly concise style, and expressed himself in a language of his own. His only extensive work, Traité des Sections Coniques, has survived through a transcription by Philippe de la Hire, who felt compelled to add a glossary of terms. There we learn that "navel" and "burning point" mean "focus," that "roll" denotes a cylindric or conic solid, whereas two different words, "column" and "horn," are used for the cylindric and the conic surface. The conic sections themselves are referred to as "the border of a roll cut." Other manuscripts were edited by Abraham Bosse, a student of Desargues who was also a sculptor, and profited from his teacher's attention towards the applications of geometry to art and architecture. Desargues wrote treatises on perspective, sundials, on the cutting of stones, on the mechanical applications of epicycloids, and he also designed buildings. He probably contributed to the construction of the dam in La Rochelle, by order of Cardinal Richelieu, with whom he was familiar, as we are told by Descartes, who was his friend and correspondent on scientific and philosophical topics.

Montucla (1960, p. 75), while despising Bosse's edited works as "barbaric" and "ridiculously lengthy," mentions a house supported by a spiral staircase that Desargues built in Lyon (and was preserved until 1844) as an authentic miracle of balance.

Desargues conceived projective geometry as a natural extension of Euclidean geometry in which parallel lines meet at infinity, sizes can vary as long as proportions are kept, and shapes are considered to be one with the totality of shadows they can cast: exactly what is needed in perspective design, where each object appears deformed according to the point of observation. Thus the plane sections of a cone are nothing but the different images projected by a light source on a wall when its inclination varies. In this framework, a circle is equivalent to an ellipse, which becomes a parabola as soon as the intersection point of the axis of the light cone with the wall ends up in infinity.

The geometric works of de la Hire, Pascal, and Poncelet were mainly based on Desargues' revolutionary intuitions.

de la Hire, Desargues' Configuration, Desargues' Theorem , Pascal, Poncelet

Additional biographies: MacTutor (St. Andrews)