‎"CAUCHY, AUGUSTIN. - CAUCHY'S THORY OF EQUIVALENCES.‎
‎Mémoire sur une nouvelle théorie des imaginaires, et sur les racines symboliques des équations et des équivalences.‎

‎(Paris, Bachelier), 1847. 4to. Without wrappers. In ""Comptes rendus hebdomadaires des séances de l’Académie des sciences"", Vol. 24, No 26. Pp. (1117-) 1160. (Entire issue offered). Cauchy's paper: pp. 1120-1130.‎

Reference : 47261

‎First apperance of this impiortent paper in which Cauchy presents his theory of algebraic equivalences where imaginary numbers were regarded as equivalent classes of polynominals with real coefficients modulo (X2 + 1).The paper gave rise to a heated debate in the Academy (see Bruno Belhoste ""Augustin-Louis Cauchy. A Biography."" pp. 210 ff.).""Augustin Louis Cauchy... objects to the use of complex or imaginary numbers and finds a method of eliminating i (the square root of negative 1) by constructing residues to the modulus X2 + 1. These residues have the formal properties of the complex number system, with x replacing i."" (Parkinson ""Breakthroughs, 1847 M).‎