Paris: Gauthier-Villars, 1865. First edition. In this work Chasles studies the properties of conic sections using the methods of projective geometry. He also includes many of his own original results on enumerative geometry (counting the number of solutions to geometric problems).
A very good copy in contemporary half calf of his sequel to the ' Géométrie Superiéure'. "Chasles wrote two textbooks for his course at the Sorbonne. The first of these, the 'Traité de Géométrie Supérieure (1852), is based on the elementary theories of the cross ratio, homographic ranges and pencils, and involution ... The second text, the 'Traité des Sections Coniques' (1865), applied these methods to the study of the conic sections. This was a subject in which Chasles was interested throughout his life, and he incorporated many results of his own into the book . For example, he discussed the consequences of the projective characterization of a conic as the locus of points of intersection of corresponding lines in two homographic pencils with no invariant line, or dually as the envelope of lines joining corresponding points of two homographic ranges with no invariant point ... The book also contains many of Chasles's results in what came to be called enumerative geometry. This subject concerns itself with the problem of determining how many figures of a certain type satisfy certain algebraic or geometric conditions. Chasles considered first the question of systems of conics satisfying four conditions and five conditions. He developed the theory of characteristics and of geometric substitution. The characteristics of a system of conics were defined as the number of conics passing through an arbitrary point and as the number of conics tangent to a given line. Chasles expressed many properties of his system in formulas involving these two numbers and then generalized his results by substituting polynomials in the characteristics for the original values." (DSB).
8vo, contemporary half calf, xi, (3) ,368 pp. and 5 folding plates.