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.
What to read after History of Modern Mathematics?
You can find similar books in the "Read Also" column, or choose other free books by Smith, David Eugene, 1860-1944 to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
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.
What to read after History of Modern Mathematics?
You can find similar books in the "Read Also" column, or choose other free books by Smith, David Eugene, 1860-1944 to read onlineMoreLess
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