99 
FROBENIUS—GEODESIC. 
Frobenius, G. : linear differential equations, xn, 394. 
Frost, P. : curves of curvature near umbilicus, vn, 330—1. 
Fuchs, L. : Schwarzian derivative and polyhedral functions, xi, 149 ; linear differential equations, xn, 
394, 453. 
Function: the term “derivational,” i, 63; transformation of bipartite quadric, n, 497—505; relation 
among derivatives of, x, 590—2; octahedron, xi, 128—9; general theory of, xi, 439—41; linear, xi, 
492 ; in Ency. Brit., xi, 522—42, (introductory, xi, 522—3 ; known functions, xi, 523—37 ; functions 
in general, xi, 537—41 ; calculus of, xi, 541—2) ; two invariants of quadri-quadric, xm, 67—8 ; on 
the modular x<u, xm, 338—41. 
Functional Determinant : the term, n, 319, iv, 607. 
Functional Equation : theorem of Abel, iv, 5—6. 
Functions: doubly-periodic, n, 150—63; notation of algebraic, n, 185—8; al(#) of Weierstrass, v, 
33—7 ; homotypical, v, 50 ; rhizic, ix, 34 ; tests for dependence of, x, 97 ; early history of theory, 
xi, 451—5 ; values of symmetric, xm, 318—21 ; on lacunary, xm, 415—7 ; (see also Schwarzian 
Derivative, Generating Functions, Symmetric Functions). 
Fundamental Notions : in Mathematics, xi, 434—8, 442—5. 
Fuss, P. H. v.: porism formula, n, 90; in-and-circumscribed polygon, n, 140, v, 21—2. 
Galileo : and dynamics, xr, 447. 
Galois, E. : groups and permutations, n, 134 ; groups, xi, 133, xm, 533 ; theory of numbers, xi, 457, 
593, 614 ; theory of equations, xi, 518—9, 520, 521 ; biographical notice, xi, 543. 
Gamma Function: theory, i, 309—16, 588; a double infinite series, ii, 8; the term, xi, 534; (see also 
Definite Integrals). 
Gaultier, L. : systems of circles, hi, 113; radical axis, xi, 465. 
Gauss, J. K. F. : determinants, i, 64 ; linear transformations, i, 585 ; attraction of ellipsoids, hi, 25—8, 
149—53; central forces problem, iv, 520, 588; relative motion, iv, 534; binary quadratic forms, 
v, 618 ; pentagramma mirificum, vn, 37—8 ; Theoria Motus, vn, 414 ; geodesic lines on quadric 
surface, vm, 156—61; potential of ellipse, ix, 281—2; epispheric integrals, ix, 321, 410—17; mathe 
matical tables, ix, 466—7, 470, 472, 475—7, 488 ; roots of unity, xi, 60 ; lemniscate, xi, 64 ; 
calculation of log 2, xi, 70 ; geodesic curvature, xi, 323—4 ; his theory of surfaces, xi, 331—6 ; 
imaginary variables, xi, 439 ; attractions, xi, 448 ; theory of equations, xi, 455, 504, 516 ; theory of 
numbers, xi, 455, 599, 603; gamma function, xi, 534; biographical notice, xi, 544—5; multiple algebra, 
xii, 471—2; roots of algebraic equation, xm, 35; orthomorphosis, xm, 191; application of surfaces 
to each other, xm, 253—64. 
Geiser, C. F. : quartic and quintic surfaces, vn, 252 ; theorem of Cotterill, ix, 506. 
Generating Functions: of symmetric functions, Borchardt’s, ii, 417, 421—3; connected with covariants, 
ix, 537—42; of quintic, x, 339—400; of quartic, x, 341; of sextic, and binary sextic, x, 394—400; 
of binary septic, x, 408—21 ; seminvariants of a given degree, xm, 306—8. 
Generation : of bicircular quartic, x, 223—6. 
Generator : the term, v, 169—70, 173—9, 181 ; nodal, of scrolls, v, 169—70, 179—81. 
Generatrix : and the absolute, xm, 481—9, 501. 
Genese, R. W. : theory of envelopes, xi, 50—1. 
Genus of Curve : (Geschlecht), after Riemann, v, 467, 517, 619. 
Geodesic Curvature : xi, 323—30. 
Geodesic Lines : property of, hi, 38 ; on oblate spheroid, vn, 15—25 ; on ellipsoid, vn, 34—5 ; in Ency. 
Brit., xi, 628, 636—7 ; of pseudosphere, xii, 220—38 ; wave surfaces, xm, 252 ; (see also Ellipsoids). 
Geodesic Lines, in particular on quadric surface, memoir : vm, 156—78, 188—99 ; preliminary formulae, 
vm, 156—8 ; general theory of them on a surface, vm, 159—62 ; circular curves are geodesics, vm, 
162; chief lines not in general geodesics, vm, 163; special form of geodesic equation, vm, 163—4; 
13—2