BRIANCHON, Charles-Julien. Mémoires sur les lignes du second ordre : faisant suite aux recherches publiées dans les journaux de l'école royale polytechnique.
Paris: Bachelier, 1817. First edition.

An expositon of his results on conics. "Brianchon’s fame rests ultimately on one theorem. In 1639 Pascal had proved that 'If all the vertices of a hexagon lie on a circle, and if the opposite sides intersect, then the points of intersection lie on a line.' He then boldly extended this result to a hexagon inscribed in any conic, since he recognized that his theorem was projective in nature. Oddly enough, it took 167 years before someone else—Brianchon—realized that since the theorem is projective in nature, its dual should also be true. Simply stated, Brianchon’s theorem is 'If all the sides of a hexagon are tangent to a conic, then the diagonals joining opposite vertices are concurrent.' the theorem is useful in the study of the properties of conics and—if the hexagon is specialized in various ways—for the study of properties of pentagons, quadrilaterals, and triangles." (D.S.B., Vol. 2, pp.454-455).

8vo: 210 x 135 mm. Uncut, contemporary plain blue wrappers (chipped, a few tears repaired), unopened. 67 pp. and 4 folding engrvaed plates.