An introduction to the modern theory of equations, by Florian Cajori.

INDEX

239

Quartic, cyclic, 198; Euler's solu- Sturm's theorem, 50, 51; applied to
tion, 71; groups of, 172, 173; in quartic, 56.
the Galois theory, 185; nature of Sub-groups, 120; index of, 122; of
roots, 56; removal of second prime index, 124.
term, 37; symmetric functions Substitutions, 104; cyclic, 107;
of roots, 91; when solvable by even and odd, 111; identical,
square roots, 72. 106; inverse, 106; laws of, 105;
Quintic, 186, 227, 229, 232, 233. product of, 105.
Substitution groups, see Groups.
Radicals, solution by, 60. Sylvester, 50.
Reciprocal equations, 33; depres- Sylvester's method of elimination,95.
sion of, 81. Symmetric functions, 13, 84, 114;
Reducibility, 134, 135, 139. fundamental theorem, 87; elimiReducing cubic, 72. nation by, 93.
Regular polygons, inscription of, Symmetric group, 114.
20. Synthetic division, 3.
Resolvents of Lagrange, 129.
Resultants, 92. Taylor's theorem, 19.
Rolle's theorem, 49. Transcendental numbers, 137.
Roots, 2; complex, 6, 42, 58, 67, Transpositions, 109.
232; fractional, 61; fundamental Trigonometric solution of irreducitheorem, 26; incommensurable, ble case, 70; of binomial equa61; integral, 62; multiple or equal tions, 74, 82, 83.
roots, 21, 53, 142; of unity, 76, Trisecting an angle, 207, 208.
198; primitive, 78; primitive con- Tschirnhausen's transformation, 99,
gruence roots, 199; reciprocal, 33. 102.
Ruffini, P., 233.
Runge, C., 229. Unity, roots of, 76, 198; primitive
roots of, 78.
Self-conjugate sub-groups, 122.
Simple groups, 122. Waring, 50.

Smith, D. E., 206.
Solvable equations, 223.
Sturm, 50.

Weber, H., 29, 134, 228, 231.
Zeuthen, 233.

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