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

INDEX
(The numbers refer to pages.)

Abel, 233.
Abelian equations, 210.
Abelian groups, 210.
Adjunction, 135, 151, 219.
Algebraic numbers, 136.
Algebraic solutions, 60, 219; of
cubic and quartic, 68.
Angle, trisection of, 207, 208.
Bachmann, 206.
Ball, 233.
Beman, W. W., 206.
Binomial equations, 74, 219.
Biquadratic, see Quartic.
Bjerknes, C. A., 233.
Budan, 50.
Burkhardt, 233.
Burnside and Panton, 79, 233.
Cantor, M., 233.
Cardan's formula, 69.
Carvallo, M. E., 67.
Cole, F. N., 189.
Complex roots, 6, 42, 58, 67, 232.
Composite sub-groups, 123.
Conjugate sub-groups, 122.
Constructions by ruler and compasses, 202.
Continuity of f(x), 25.
Cross-ratio, 100, 127.
Cube, duplication of, 207.

Cubic, algebraic solution, 68; cyclic:
196; equation of squared differences of, 38; irreducible case, 69,
208; nature of roots, 41; reducing cubic, 72; removal of second
term, 36.
Cyclic equations, 187, 196, 198,
220.
Cyclic function, 115, 127, 128, 133.
Cyclic group, 115, 128, 132, 133.
Cyclotomic equations, 142, 198.
Delian problem, 207.
De Moivre's theorem, 24.
Descartes, 50.
Descartes' Rule of Signs, 7, 50.
Dialytic ilethod of elimination, 95.
Discriminant, 110; of quadratic,
97; of cubic, 40; of quartic, 59;
of f(z)- 0, PcO,!,.
Division of the ciricle, 75, 203-206.
Domain, defined, 134; conjugate,
143; degree of, 142; Galois, 153;
normal, 142, 150; primitive, 144;
substitutions of, 160.
Duplication of the cube, 207.
Easton, B. S., 233.
Eisenstein's theorem, 141.
Eliminants, 92.
Equal roots, 21, 53, 142.

237