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

238

INDEX

Equations, Abelian, 210; algebraic, Horner's method, 63.
2; algebraic solution of, 219;
binomial, 74, 219; cubic, 36, 38, Imaginary roots, 6, 42, 58, 67,
41, 68, 69, 72, 196, 208; cyclic, 232.
187, 220; cyclotomic, 142; irre- Imprimitive group, 116, 127.
ducible, 137; metacyclic, 223; Invariant sub-groups, 122.
quadratic, 184; quartic, 185; Irreducible case in cubic, 69, 208.
quintic, 186, 227, 229, 232, 233;
reciprocal, 33. Klein, F., 206, 233.
Euler's cubic, 71. Kronecker, 187, 233.
Euler's method of elimination, 94.
Euler's solution of quartic, 71. Lagrange, 233; resolvents of, 129;

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Fine, H. B., 233.
Fink, 233.
Fourier, 50.
Function, def. 1; alternating, 115;
"belongs to," 115, 124, 125;
cyclic, 115,127, 128; derived, 18;
Sturm's, 50; resolvents of Lagrange, 129; symmetric, 13, 84,
114.
Galois, 143, 176, 233.
Galois' theory of numbers, 134; domain, 153; resolvent, 155, 156,
reduction of, 174, 178; groups,
164, determination of, 169.
Gauss, 26, 206; Lemma, 138.
Graphic representation, 15, 23, 75.
Groups, 112; Abelian, 210; alternating, 115; composite, 123;
cyclic, 115, 128, 132, 133; degree
and order of,. 113; Galois, 164;
index of, 122; list of, 118, 119;
normal sub-groups, 122; 124;
primitive and imprimitive, 116;
simple, 122; sub-groups, 120; symmetric, 114; transitive and intransitive, 116.
Hermite, 137.
Historical references, 233.
Homographic transformation, 99.

theorem of, 176.
Lindemann, 137.

Marie, 233.
Matthiessen, L., 186.
McClintock, E., 67, 230.
Metacyclic equations, 223, 227.
Miller, G. A., 233.
Moritz, 26.
Multiple roots, 21, 53, 142.
Netto, 189, 218, 228, 229.
Newton, 50.
Newton's formula for sums of powers, 84.
Newton's method of approximation,
66.
Normal domain, 142, 145, 150.
Normal equations, 149, 151.
Normal sub-groups, 122; of prime
index, 124.
Numbers, algebraic, 136; conjugate,
144; primitive, 144, 147; transcendental, 137.
Panton, see Burnside and Panton.
Picard, 233.
Pierpont, J., 233.
Primitive congruence roots, 199.
Primitive domains, 144, 147.

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Quadratic equation, 184.