Girard Desargues

1591-1661

French Mathematician

The significance of Girard Desargues's work did not become apparent until long after his death; indeed, at the time of his passing in 1661, it would have been hard to imagine that anyone would remember him a generation later. His ideas about geometry broke with Euclidean tradition, and thereby aroused the criticism of no less a figure than his acquaintance René Descartes (1596-1650); yet Desargues is today recognized as a prophet of projective geometry nearly two centuries ahead of his time.

Desargues's father Girard, who with his wife Jeanne Croppet had nine children, served as a tithe collector in Lyon. In an era when the church still dominated political affairs, this was the equivalent of a tax collector; and as in the time of Christ, it appears that collectors of the church's tax fared well: the Desargues family owned several houses, a chateau, and a vineyard. Little is known about the early life of the younger Girard, born on February 21, 1591, but it appears that by 1626, when he was 35, he had gone to work in Paris as an engineer.

His career was an intriguing one. At one point, Desargues proposed a scheme to pump waters from the Seine throughout Paris—an idea which, like his geometry, was ahead of its time. Later, as an architect during the 1640s and 1650s, he designed a number of houses in Paris, applying his concepts on perspective to the design of staircases. Employed by the French government under Cardinal Richelieu, he also assisted in the 1627-28 siege of the Huguenot stronghold at La Rochelle, where members of the Protestant sect were forced through starvation to capitulate. It appears that during the siege, he met Descartes, and by 1630 had become part of a Parisian intellectual circle that also included Marin Mersenne (1588-1648) and Etienne Pascal (1588-1651). In time, Desargues would exert a powerful influence on Pascal's son Blaise (1623-1662), who was destined to shine brighter than any of the group other than Descartes.

During the 1630s, Desargues published several works, one of which was particularly notable. Traité de la section perspective (Treatise on the Perspective Section, 1636), challenged existing ideas of perspective, and presented what came to be known as Desargues's theorem. According to the latter, two triangles may be placed such that the three lines joining corresponding vertices meet in a point, if and only if the three lines containing the three corresponding sides intersect in three collinear points. This theorem, which holds true in either two or three dimensions, would provide an early foundation for what came to be known as projective geometry.

In 1639, Desargues published Brouillon project d'une atteinte aux événements des recontres d'une cône avec un plan (Proposed Draft of an Attempt to Deal with the Events of the Meeting of a Cone with a Plane). As its title suggests, the essay dealt with conic sections, and presented what amounted to a unified theory of conics. As with Desargues's other groundbreaking ideas, however, those in Brouillon were slow to find acceptance, in part because of the highly arcane terminology the author used, substituting tree, stump, and other botanical terms for various geometrical constructs.

Desargues meanwhile came under attack from Descartes for what the latter perceived as an attack on geometry—which indeed Desargues's work was, though what was really threatened was the limited Euclidean worldview that then dominated. Jean Beaugrand (1595-1640) charged that Desargues had lifted his ideas from the ancient Greek mathematician Apollonius of Perga (262-190 b.c.), and the two exchanged attacks in print for many years. His ideas on perspective also won Desargues a number of detractors outside the world of mathematics, including artists, other architects, and even the stonecutters' guilds, whose established method of performing their job was under challenge.

Desargues, who also pioneered a method of using cycloidal or epicycloidal teeth for gear wheels, died a nearly forgotten man in September 1661. Had it not been for the efforts of his friend, the engraver Abraham Bosse, his writings might have been lost. Only with the rediscovery of Desargues's ideas by Jean-Victor Poncelet (1788-1867) in the nineteenth century did the significance of his work for projective geometry become known.

JUDSON KNIGHT