Girard Desargues

Girard Desargues (1591–1661) was a French mathematician and engineer whose work helped establish projective geometry, especially through results on perspective and conic sections.

Projective geometry: A branch of geometry studying properties unchanged by projection, including incidence and alignment. Desargues’s work helped establish this broader geometry of projection and perspective.
Blaise Pascal: A French mathematician, physicist, and philosopher whose early work included a theorem on hexagons inscribed in conics. Pascal’s conic theorem extended projective ideas developed in Desargues’s work.
Marin Mersenne: A French polymath who organized an influential correspondence network among seventeenth-century scholars. Mersenne’s circle circulated Desargues’s mathematical ideas.
Desargues configuration: A configuration of ten points and ten lines in which each line contains three points and each point lies on three lines. It encodes the incidence pattern behind Desargues’s theorem.
Perspective (graphical): A method for representing three-dimensional space on a plane through projected lines and vanishing points. Desargues treated perspective as a geometric subject, not merely an artistic technique.
Pascal's theorem: A theorem stating that the three pairs of opposite sides of a hexagon inscribed in a conic meet on one line. Pascal explicitly built on Desargues’s approach to conics and projection.
Abraham Bosse: A French printmaker and writer who published influential manuals on perspective and engraving. Bosse disseminated Desargues’s perspective methods to artists and craftspeople.
Desargues's theorem in a plane: The planar statement that perspective triangles have collinear intersections of corresponding sides. This is the theorem’s familiar two-dimensional form.
Conic section: A curve formed by intersecting a plane with a cone, including ellipses, parabolas, and hyperbolas. His projective methods unified the study of these curves.
Jean-Victor Poncelet: A French mathematician whose nineteenth-century work helped revive projective geometry. Poncelet helped restore attention to a tradition Desargues had pioneered.

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Desargues's theoremBroader topic: The theorem bears his name and appeared in his work on conic sections.