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.

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).

Order-nr.: 47261