QUADRATIC-QUANTICS. 
122 
Quadratic Residues: Eisenstein’s geometrical proof, hi, 39—43. 
Quadratic Transformation of Binary Form: vin, 398—400; (see also Transformation). 
Quadratics: resultant of three ternary, and invariant of biternary, iv, 349—58. 
Quadric Cones: of six given points, v, 4—6; through given points, x, 575. 
Quadric Curves: v, 70—2. 
Quadric Equations: transformation of two, i, 428—31, in, 129—31; automorphic linear transformation 
of, n, 497—505; solution by radicals, x, 9 ; two related, xi, 37. 
Quadric Integral: due to Aronhold, xii, 162—9. 
Quadricone: the term, vi, 334, 585, vii, 264. 
Quadricovariant: of quantic, ii, 520; or Hessian, ii, 545; the term, iv, 606. 
Quadrics: through nine points, i, 425—7; developable from two, i, 486—95; homographic transformation 
into itself, n, 105—12, 117, 133—7; theorem on surfaces, in, 115—7; equation of differences for, 
iv, 242; the term, iv, 604; sections of, v, 133—4; through three lines, vii, 177; in hyperdimensional 
space, ix, 79—83; covariants of, ix, 537—42; envelope of family of, x, 589; correspondence of 
confocal Cartesians with right line of a hyperboloid, xii, 587—9; (see also Binary Quadrics . 
Quadric Seminvariants: generating functions of, xin, 306. 
Quadric Surfaces: «-dimensional geometry, i, 62; diametral planes of, i, 255—8; centres of similitude, 
i, 329—31; note, i, 421—2, 589; abstract of memoir by Hesse, i, 425—7; conics inscribed in a, 
i, 557—63; envelope of certain, vm, 48—50; inversion, viii, 67—71; problem, and hypothetical 
theorems, vm, 550; and four-dimensional space, ix, 246—9; a system of, x, 269; Jacobian of, x, 
568; in Ency. Brit., xi, 576—9, 632; twisted cubics on, xii, 307—10; focals of, xra, 51—4; reciprocal 
lines, xm, 58—9; (see also Geodesic Lines). 
Quadric Transformation: between planes, vn, 213—5, 219—21, xii, 100—1 ; (see also Transformation). 
Quadri-cubic Curves in Space: v, 16. 
Quadricuspidal: the word, vii, 51. 
Quadrifactions: the term, ix, 426. 
Quadrilateral: and ellipse, v, 604; inscribed in bicircular quartic, x, 231—5; inscribable in circle, 
x, 578. 
Quadrinvariant: of binary quartic, first occurrence, i, 93; of quantic, n, 516; the term, iv, 606; 
of quadriquadric function, xm, 67—8. 
Quadriquadric: the term and kinds, v, 10, vii, 99. 
Quadriquadric Curves: in space, v, 17; on, v, 282; sextic torse for cuspidal edge having, x, 68—72; 
Abel’s theorem, xii, 186—9, 292—8, 321—5 ; and elliptic functions, xii, 292—8, 321—5. 
Quadriquadric Function: two invariants of, xm, 67—8. 
Quadriquadric Transformation: between spaces, vii, 229—30; (see also Transformation). 
Quadrispinal: the term, vii, 65. 
Quantics, Introductory Memoir: n, 221—34, 598—601. 
Quantics, Second Memoir: n, 250—75; numerical tables, n, 276—81. 
Quantics, Third Memoir: n, 310—35. 
Quantics, Fourth Memoir: n, 513—26 ; definitions, n, 513—5; covariants and invariants of degrees, 
two, three, four, n, 515—20; calculation of discriminant, n, 520—2; the catalecticant, lambdaic, 
and canonisant, n, 522—3; bezoutiants, cobezoutiants, n, 524—6. 
Quantics, Fifth Memoir: n, 527—57, 604—6; the single quadric, n, 527—9 ; two or more, and 
theories of harmonic relation and involution, n, 529—40 ; cubics, n, 540—5 ; quartics, ii, 545—56. 
Quantics, Sixth Memoir: analytical theory of binary and ternary, n, 561—83; general theory of dis 
tance, ii, 583—92; its style, vm, xxvii. 
Quantics, Seventh Memoir: chiefly ternary cubics, iv, 325—41; tables, iv, 333—41. 
Quantics, Eighth Memoir: vi, 147—90; introductory, iv, 147—8; binary quintic, covariants and 
syzvgies of degree 6, vi, 148—53; formulae for canonical form, vi, 153—4; 18-thic invariant, vi,