BRIANCHON, CHARLES-JULIEN

born Dec. 19, 1783, Svres, France died April 29, 1864, Versailles French mathematician who derived a geometrical theorem (now known as Brianchon's theorem) useful in the study of the properties of conics (circles, ellipses, parabolas, and hyperbolas) and who was innovative in applying the principle of duality (interchangeability) to geometry. In 1804 Brianchon entered the cole Polytechnique, Paris, where he became a student of the noted French mathematician Gaspard Monge. While still a student, he published his first paper, Mmoire sur les surfaces courbes du second degr (1806; Memoir on Curved Surfaces of Second Degree), in which he recognized the projective nature of a theorem of Blaise Pascal, and then proclaimed his own famous theorem: If a hexagon is circumscribed about a conic (all sides made tangent to the conic), then the lines joining the opposite vertices of the hexagon will meet in a single point. Brianchon graduated first in his class in 1808 and joined Napoleon's armies as a lieutenant in the artillery. Though his courage and ability distinguished him in the field, particularly in the Peninsular campaigns, the rigours of field service affected his health. In 1818 he gained a professorship in the Artillery School of the Royal Guard, Vincennes, where his mathematical work was slowly replaced by other interests.