89 
CURVES—CYCLOID. 
curvature at double point, iv, 466—9; higher singularities, v, 424—6, 520—8, 619; correspondence 
of points on, v, 542—5; transformation, vi, 1—8, 593, vm, 387; notion of, of given order, xm, 
79—80. 
Curves, Plane, sextactic points of: v, 221—57, 618—9; condition for point, v, 222—5; notations and 
remarks, v, 225—6; first transformation, v, 226; second, v, 227—8; third, v, 228—9; fourth 
and final form, v, 229—33; application to cubic, v, 233—5; proof of identities, v, 235—7; Jacobian 
formula, v, 237—8; proofs of equations and identities, v, 239—47; appendix, v, 247. 
Curves, Poloid: iv, 571. 
Curves, Rhizic: ix, 34. 
Curves, Serpoloid: iv, 571. 
Curves, Sextic: vn, 256—7, vm, 138—44, x, 612. 
Curves, Symmetric: i, 473. 
Curves, Theory of: and elimination, i, 337—51, v, 162—7, 416—20; evolution, xi, 449—51, xii, 102—3, 
290—1. 
Curves, Theory of, and Torse: vm, 72—91; explanations and notation, vm, 72—4; Pliicker-Cayley 
equations, vm, 74, 75—6, 80—1; Salmon-Cremona equations, vm, 74, 76—9, 87—91; geometrical 
theory of foregoing relations, vm, 79—80; tables, vm, 81—4; nodal curve x, vm, 84—7. 
Curves, Three-bar: ix, 551—80, 585. 
Curves, Transformations of: i, 471—5, 476—SO; scalene, ix, 527—34. 
Curves, Triangular: vn, 59. 
Curves, Twisted Quartic: xn, 428—31. 
Curves which satisfy given conditions: vi, 191—262, 594, vn, 40; Introductory, vi, 191; previous 
memoirs, vi, 191—2; quasi-geometrical representation of conditions, vi, 193—200; Chasles’ and 
Zeuthcn’s researches, vi, 200—26; extensions of de Jonquieres, vi, 226—42; form of equation of curves 
of a series of given index, vi, 242—3; line-pairs which pass through three given points and touch 
a given conic, vi, 244; conics which pass through two given points and touch given conic, vi, 
245—9; conics which touch cuspidal cubic, vi, 249—53; conics which have contact of third order 
with given cuspidal cubic and double contact with given cubic, vi, 253—6; Zeuthen’s forms for 
characteristics of conics which satisfy four conditions, vi, 256—8; question from de Jonquieres’ 
formula, vi, 258—62; the principle of correspondence, vi, 263—91; (introductory, vi, 263—4; 
correspondence of two points on a curve, vi, 264—8; application to conics which satisfy given 
conditions, one at least arbitrary, vi, 268—71; five conditions of contact with a given curve, 
vi, 272—91). 
Curve Tracing: Cayley’s liking for, vm, xxxix; mechanism, vm, 179—80, xm, 515—6; importance, xi, 
461; order of, xi, 461. 
Curvilinear Coordinates: xi, 330, xn, 1—18; surfaces divisible into squares, vm, 146; geodesic lines, 
vm, 156—67; curves of curvature, vm, 264—8; orthogonal surfaces, vm, 269—91. 
Cusp: of Cartesian at circular points at infinity, i, 589; synonymous with spinode, n, 28, iv, 22, 27; 
of second kind or node-cusp, v, 265—6, 618; order of plexus for, v, 309—12; the term, xi, 468. 
Cuspidal: defined, v, 403, 551, vn, 244. 
Cuspidal Conic: of centro-surface, vm, 352—7. 
Cuspidal Cubic: vn, 561. 
Cuspidal Curves: and cubic surfaces, vi, 450; (see also Cubic Surfaces, Surfaces). 
Cuspidal Isochronic : the term, vn, 473. 
Cuspidal Locus: in singular solutions, vm, 533. 
Cyc: the abbreviation in groups, xm, 119. 
Cyclide: of Dupin, v, 467, xn, 615; the term, vn, 246, vm, 262, ix, 64—5; and anchor ring, ix, 
18; on, ix, 64—78; the parabolic, ix, 73—8; in Ency. Brit., xi, 634. 
Cycloid: the term, xi, 447. 
C. XIV. 
12