CUBIC-CURVES. 
88 
22; 12 — 2B 3 , vi, 422—6 ; 12-B 4 -C 2 , Vi, 426—8; 12-B S , vi, 429—30; 12-U 6 , vi, 431—3; 
12-^3-2(72, VI, 433—6; 12-B S -C 2 , VI, 437—9; 12 - U 7 , VI, 439—40; 12-4^, VI, 441—2; 
12 —25—(7 2 , vi, 443—4; 12-5 4 -2(7 2 , vi, 445—6; 12-B 6 -C 2 , vi, 447—8; 12— U s , vi, 448—9, 
451—5; 12-35 3 , vi, 449—50; synopsis of foregoing, vi, 450; cubic scrolls, vi, 451. 
Cubic Surfaces: triple tangent planes, i, 445—56, 589; skew, v, 90—4; delineation of scrolls, v, 110—2; 
nodal curve of developable from quartic equation, v, 135—7; theory, v, 138—40; five given 
lines on, vn, 177—8; double sixers, vn, 316—29; and tetrahedra, vn, 607; Wiener’s model with 
27 real lines, vm, 366—84; in Ency. Brit., xi, 633. 
Cubic Transformation of Elliptic Functions: hi, 266—7, vn, 44—6, x, 46, 58, xn, 518—22, 555, 
556—7 ; geometric illustration, ix, 522—6. 
Cubi-Cubic Curves: in space, v, 18—9. 
Cubinvariants: of binary quartic, i, 94; of quantic, n, 516; the term, iv, 606; of quadri-quadric 
function, xm, 67—8. 
Cuboid: potential of, ix, 272, 274—5, 278—80. 
Cumulant: the word, iv, 600—1. 
Cunningham, A. : on number of terms in a determinant, x, 579—80. 
Curtate: the term, xi, 155. 
Curvature: lines of, on ellipsoid, i, 36—9 ; of plane curve at double point, iv, 466—9; of surfaces, 
iv, 466—9 ; geodesic, xi, 323—30; (see also Curves of Curvature, Orthogonal Surfaces). 
Curves: and developables, i, 207—11, 485, 586—7, 589; and two dimensional geometry, n, 569—83; 
partial branch of, v, 425; reciprocation, v, 505—10; representation by cone and monoid surface, 
v, 552 ; nodal, spinode and cuspidal, of cubic surfaces, vi, 450, 595 ; and space of m dimensions, 
vi, 456—7 ; correspondence of two points on, vn, 39; graduation, vn, 426; mechanical description, 
of, vm, 138—44, 147—50, 151—5, x, 576; bicyclic chuck for, vm, 209—11; penultimate forms, 
vm, 258—61, 262—3; property of curve and torse, vm, 520—1; coordinates and equations, x, 
546; degenerate forms, xi, 218—20, 487—9; abstract geometry, xi, 441—2; in Ency. Brit., xi, 
460—89, 572—3, 579—80; and theory of equations, xi, 501 ; and function, xi, 540—1 ; and solid 
geometry, xi, 569; quadrature of, xi, 641—2; minimal surfaces, xm, 41; orthotomic, of a system 
of lines in a plane, xm, 346—7 ; (see also Correspondence, Cubic Curves, Nodal Curves, Polyzomal 
Curves). 
Curves, Algebraic: i, 46—54, 584. 
Curves, Bicursal: vm, 181—7. 
Curves, Classification of: v, 613—7 ; (see also Cubic Curve Classification). 
Curves, Excubo-quartic: v, 282. 
Curves in Space: analytical representation, iv, 446—55, 490—5, 616—8, vn, 66, xi, 9—13; defined by 
conoid and monoid surfaces, v, 7—20, 552, 553, 613; quartic, v, 11—5; quintic, v, 15—6, 24—30, 552, 
553, 613; quadri-cubic, v, 16; quadri-quartic, v, 17; cubi-cubic, v, 18—9; Halphen’s characteristic 
n in theory of, xm, 468—72. 
Curves, Intersections of: i, 25—7, 583, xii, 500—4; real, ix, 21. 
Curves of Curvature: near umbilicus, vn, 330—1; on surfaces, vm, 97—8, 145—6, 264—8; Ency. 
Brit., xi, 628, 635—6; wave surface, xii, 249; surfaces with spherical, xn, 601—38. 
Curves of Striction: i, 234. 
Curves, Opposite: v, 468. 
Curves, Parallel: envelopes and surfaces, iv, 123—33, 152—7, 158—65; and evolutes, vm, 31—5; 
theory of, x, 260; the critic, in solar eclipses, x, 311—5. 
Curves, Pedal: v, 113—4. 
Curves, Penultimate Quartic: vm, 526—8. 
Curves, Penumbral: geometrical theory of projection, vn, 483, 488—9, 489—92. 
Curves, Plane: double tangents of, iv, 186—206; conic of five-pointic contact of, iv, 207—39;