Mémoir sur les surfaces courbes du second degré

Charles-Julien Brianchon's 1806 memoir, "M\u00e9moire sur les surfaces courbes du second degr\u00e9," explored curved surfaces of the second degree, which are also known as quadric surfaces. These are surfaces defined by a polynomial equation of the second order. The simplest of these is a plane, while surfaces of order two include ellipsoids and hyperboloids. Brianchon's work also recognized the projective nature of a theorem by Blaise Pascal and led to Brianchon's theorem, which relates to hexagons circumscribed about a conic section. This theorem is significant in geometry and is the dual of Pascal's theorem.