‎"ROLLE, (MICHEL). - DISCOVERING PROBLEMS IN CARTESIAN ANALYTICAL GEOMETRY.‎
‎Eclaircissemens sur la Construction des Egalitez. (+) Eclaircissemens....Second memoir.‎

‎(Paris, Jean Boudot, 1709 a. 1711). 4to. Without wrappers. Extracted from ""Mémoires de l'Academie des Sciences. Année 1708"" and Annèe 1709. Pp. 339-365 a. 1 folded engraved plate + pp. 320-350 a. 1 folded engraved plate.‎

Reference : 45238

‎First printing of two importent papers in the further development of Cartesian analytical geometry.""The irrepressible Michel lRolle...in the Memoires of the Academie des Sciences for 1708-1709 (the papers offered), raised doubts about the correctness of the Cartesian graphical solution of equations, as he had about the validity of the calculus of L'Hospital. He pointed out that to solve f(x)= 0, one arbitrarily chooses a curve g(x,y) = 0, and, on combining it with f(x) = 0, one obtains new curves h(x,y) = 0, the intersection of which with g(x,y) = 0 furnish the solution of f(x) = 0"" and he realized that in this way extraneous solutions may be introduced. Imaginary branches further comp0licated the problem, and although Rolle sawthe difficulties, he was unable to solve them.""(Boyer ""History of Analytical Geometry"", p. 155).‎