Little is known of the early life of Desargues except that he was born in Lyons in France. He did serve as an engineer at the siege of La Rochelle (1628) and later became a technical adviser to Cardinal de Richelieu and the French government. He is said to have known René Descartes.

Around 1630 Desargues joined a group of mathematicians in Paris and concentrated on geometry. In his most famous work, Brouillon projet d'une atteinte aux événements des rencontres d'une cône avec un plan (1639; Proposed Draft of an Attempt to deal with the Events of the Meeting of a Cone with a Plane), he applied projective geometry to conic sections. Desargues' theorem states that if the corresponding points of two triangles in nonparallel planes in space are joined by three lines that intersect at a single point, then the pairs of lines that are the extensions of corresponding sides will each intersect on the same line. Blaise Pascal was greatly influenced by Desargues, whose contribution to projective geometry was not recognized until a handwritten copy of his work was found in 1845. This oversight probably arose because he used obscure botanical symbols instead of the better-known Cartesian symbolism.