History of Modern Mathematics

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For simple cases the problem goes back to Hudde (1659). Saunderson (1740) noted that the determination of the quadratic factors of a bi- quadratic expression necessarily leads to a sextic equation, and Le Sceur (1748) and Waring (1762 to 1782) still further elabo- rated the idea.
Lagrangef first undertook a scientific treatment of the the- ory of substitutions. Prior to his time the various methods of solving lower equations had existed rather as isolated artifices than as a unified theory4 Thr
...ough the great power of analy- sis possessed by Lagrange (1770, 1771) a common foundation was discovered, and on this was built the theory of substitu- tions. He undertook to examine the methods then known, and to show a priori why these succeeded below the quintic, but otherwise failed, tn his investigation he discovered the important fact that the roots of all resolvents (r^solvantes, r^- duites) which he examined are rational functions of the roots of the respective equations. To study the properties of these functions he invented a " Calcul des Combinaisons," the first * Netto, E., Theory of Substitutions, translated by Cole; Cayley, A., Equa- tions, Encyclopaedia Britannica, gth edition.

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