Desargues, Girard (1591–1661)

Summary

Desargues was born in Lyon. His father was a royal notary, and the family was clearly wealthy, with various properties in and around Lyon. Little is known about Desargues’ early life and education. By 1626 he was in Paris and moving in mathematical circles. Later, he is recorded as having regularly attended Mersenne's meetings with men such as Étienne Pascal, Mydorge, and Hardy, and probably much of his early mathematical work was produced for distribution among such contemporaries.

In 1636 he published Une methode aisée pour apprendre et enseigner à lire et escrire la musique, which was later included in Mersenne's Harmonie universelle. The same year also saw publication of Méthode universelle de metre en perspective les objets donnés réellement, in which Desargues formulated the mathematical rules of perspective that had been developed by painters and architects during the Renaissance. Desargues’ most important work, in which he set out the foundations of projective geometry, is the Brouillon project d'une atteinte aux événemens des rencontres du cone avec un plan. This “Rough Draft” is short and somewhat impenetrable; beginning with topics such as the range of points on a line, Desargues proceeds to show that conics can be discussed by means of properties that are invariant under projection. Remarkable thereby is the rigorous treatment of cases involving infinite distances. Not many copies were printed, and few apart from Blaise Pascal recognized its significance. For Descartes, Desargues’ failure to employ algebra limited the scope of his approach.

Descartes corresponded with Desargues indirectly through Mersenne and praised his articulation of the principles of gnomonics or dialing. For his part, Desargues, in 1638, joined forces with Mydorge and Hardy in defending Descartes against attacks from Roberval and Étienne Pascal during their dispute with him over Fermat's method of determining maxima and minima.

In 1640 Desargues published under the Brouillon project an essay on stone cutting and on gnomonics, showing how his graphical method was to be used as a means to simplifying the construction of sundials. This was an area of mathematical practice traditionally governed by the laws of trade guilds and is indicative of his concern for applications of mathematics.

A dispute over the publication, in 1642, of Dubreuil's La perspective pratique, in which Desargues found his method copied and distorted, led him to entrust the engraver Abraham Bosse with spreading his methods and defending his work.