103 
HESSE—HYPERBOLOID. 
Hesse, L. O.: linear transformations, I, 87, 113—6, 232—3, 584, 585, vi, 22—3, 73; cubic curves, i, 
194, ii, 399; involution, i, 259; hyperdeterminants, i, 354; abstract of memoir on quadric surfaces, 
i, 425—7; inflexions of cubic, I, 584, n, 29, hi, 48; on elimination, iv, 3; on inflexions, iv, 186, 
xi, 473; double tangents, iv, 186—7, 343—6; cubic forms, iv, 353; geometric transformation, 
vii, 121—2; bitangents of quartic curve, vn, 123—4; double theta functions, x, 177; triple theta 
functions, x, 446, 448, 451; the thirty-four concomitants of ternary cubic, xi, 342; bitangents of a 
plane quartic, xn, 76. 
Hessians: and Eisenstein’s theorem, I, 585; defined, n, 319, iv, 607, xi, 471, 474; and Pippian, n, 
381—2, 383—95, 416; the sign for, n, 541; the quadricovariant, n, 545; of quaternary functions, 
ix, 90—3; of a quartic surface, x, 274—7; (see also Qualities). 
Hexagon: and conic, problem, v, 576; theorem of inscribed, xi, 556. 
Hexagram (see Pascal’s theorem). 
Hexahedron: edges of, problem, x, 613; automorphic function for, xi, 184. 
Hierholzer, C.: cones satisfying six conditions, vm, 99; surface of eighth order, vm, 401. 
Higher Singularities of Curves (see Singularities). 
Hilbert, D.: curves in space, v, 614; abstract geometry, vi, 596. 
Hills: altitude, and roots of algebraic equation, xm, 33—7. 
Hirsch, Meyer: algebra of, n, 417, 440; partitions, vn, 577. 
Hirst, T. A.: negative pedals, iv, 164. 
History: importance of mathematical, vm, xii. 
Hodograph: isochronism of circular, hi, 262—5; Hamilton’s, iv, 520; and pedal curves, v, 113. 
Holder, O.: theory of groups, xm, 336, 533. 
Holditch, H. : caustics, n, 363. 
Holomorphic: the term, xi, 81. 
Homaloids: prepotentials of, ix, 408—9. 
Homographic Figures: matrices, n, 219; theorem, iv, 442—5. 
Homographic Function: distribution of electricity, xi, 2—6; and matrix of the second order, xi, 252—7. 
Homographic Relations: and theory of numbers, ix, 613; function of, x, 298—306; powers of, x, 305—6, 
307—9. 
Homographic Transformation: of quadric surfaces, n, 105—112; of single theta functions, xii, 337— 
43; (see also Groups, Transformations). 
Homographies : correspondence with rotations, x, 153—4, xi, 237—8. 
Homography: different classes of, n, 219—220; and quadrics, n, 536—40; ternary qualities and theory 
of, ii, 565—9, 578; of ranges and pencils, n, 578. 
Homology: of conics, i, 523, 557; the term, I, 557—8; of sets, in, 35. 
Homotypic: the term, vn, 123. 
Homotypical: the term, v, 50. 
Hopkins, W. : attractions and multiple integrals, i, 582. 
Horner, W. G.: theory of equations, xi, 499, 502. 
Hoiiel, J.: equations of motion, hi, 169, 170. 
Hudson, C.: equal roots of equations, xi, 405—7. 
Hydrodynamics: note on equations of, xm, 6—8. 
Hydrogen: trees of, ix, 427—60, 544—5. 
Hyperbola: rectangular, hi, 254, v, 554; classification, v, 354—400, vm, xxxviii; arc of, xi, 337—9; 
and cubic curves, xi, 478; in Ency. Brit., xi, 561—4; focáis of quadric surface, xm, 54; and epi- 
trochoid, xm, 82—7; tactions, xm, 150—69 ; (see also Conics). 
Hyperboloid: coordinates of, v, 72; and scrolls, vn, 65; and tractor, vn, 73—5; passing through three 
given lines, vn, 86—8; Mercator’s projection, vm, 568, ix, 237—40; deformation, xi, 66—7; in Ency. 
Brit., xi, 576—9; confocal Cartesians and right lines of, xii, 587—9.