ENCYCLOPAEDIA—EQUATIONS. 
96 
Encyclopceclia Britannica, articles from on:—Curve, xi, 460—S9; Equation, xi, 490—521; Function, xi, 
522—42; Galois, xi, 543; Gauss, xi, 544—5 ; Geometry (analytical), xi, 546—82 ; Landen, xi, 583—4; 
Locus, xi, 585; Monge, xi, 586—8; Partition of numbers, xi, 589—91; Theory of numbers, xi, 
592—616; Series, xi, 617—27; Surface, xi, 628—39; John Wallis, xi, 640—3. 
Endecadic Transformation; in elliptic functions, ix, 152—5. 
Endoscopic : the term, i, 588. 
Ennead: the term, vii, 256, vm, 566. 
Enneadianome: the term, vn, 134. 
Enneagon : in-and-circumscribed, iv, 298—303. 
Envelopes: developable of two equations, i, 486; parallel curves and surfaces, iv, 123—33, 152—7, 
158—65; defined, iv, 458, vi, 467; of circle, v, 610, vn, 591 ; and locus in regard to triangle, vi, 
72—82; depending on two circles, problem and solution, vn, 573; of plane curve, vn, 606 ; of a 
certain quadric surface, vm, 48—50; locus in singular solutions, vra, 533; problem of, vm, 491—2; 
of family of quadrics, x, 589 ; theory, xi, 50—1 ; of variable curves, xi, 475—6. 
Epicycloid: and caustic, n, 345. 
Epispheric integrals : Gauss-Jacobi theory, ix, 410—7. 
Epitrochoid : xm, 81—7. 
Equal: applied to circles, vm, 31. 
Equality: among roots of an equation, ii, 465—70, vi, 300—12; idea of, xi, 431. 
Equation of Diiferences: for equation of any degree, iv, 150—1; for equation of any order, iv, 240—61; 
tables, iv, 246—56; of all but one, of roots of given equation, iv, 276—91; and quintic equation, 
iv, 309—24, 609—16 ; and cubic equation, iv, 463—5. 
Equation, Pellian (see Pellian Equation). 
Equations: systems of spherical coordinates, i, 213—23; with quantics, defined, n, 221; auxiliary for 
quintics, iv, 309—24; determination of reciprocal, with cubic surfaces, vi, 368—70; the term, vi, 466; 
solubility by radicals, vn, 13—4; system of, problem and solution, vn, 578, 581, x, 601 ; trans 
formation, ix, 42, 48—51; on a functional equation, x, 298—306; Cassinian, problem, x, 608; Jacobian 
sextic, xi, 389—401, xn, 493—9; equal roots of, xi, 405—7; of curves, xi, 462—4; of Pliicker, 
xi, 469—73, xm, 536; in Ency. Brit., xi, 490—521, (introductory, xi, 490; determinant, xi, 490—7; 
imaginary, xi, 502—6); of right line and circle, xi, 558—61; of conics, xi, 563; seminvariants, xii, 
19—21; fundamental, and deformation of surfaces, xi, 331; note on system of, xn, 48—9; for three 
circles which cut each other at given angles, xn, 559—61, 564—70; anharmonic ratio, xn, 578—9; 
hvdrodynamical, xm, 6—8; Sylvester on ternary cubic-form, xm, 47; on soluble quintic, xm, 88—92; 
Waring’s formula for sum of with powers of roots of, xm, 213—6; sextic resolvent of Jacobi and 
Kronecker, xm, 473—9. 
Equations, Algebraic: rationalization, ii, 40—4 ; theory, n, 124; theorem that every one has a root, 
iv, 116—9; system of, iv, 171—2, vm, 29—30; in Ency. Brit., xi, 506—21; Anglin’s formula for 
successive powers of the root of, xn, 33—4; roots of one, xm, 33—7. 
Equations, Cubic (see Cubic equations). 
Equations, Modular: for transformation of order 11, xm, 38—40; for cubic transformation, xm, 64—5; 
(see also Transformation of Elliptic Functions). 
Equations of Motion: in lunar theory, xm, 206. 
Equations, Solutions of: .r 257 -l=0, i, 564—6; 6 n = 1, and theory of groups, n, 123—30, 131—2, 
iv, 88—91, x, 610; x v -1 = 0, xi, 314—6, xii, 72—3; elliptic function solution of aP + y 3 —1=0, 
xii, 35—7; the quaternion qQ-Qq' = 0, xii, 300—4, 311—3; (abed) = (oRficW), xii, 418—20; a? 17 -l=0, 
xm, 60—3. 
Equations, Theory of: synopsis, x, 3—11; Newton-Fourier method, and imaginary root, xi, 114—21, 
143; theorem of Abel’s and quintic equation, xi, 132—5; theorem in, xi, 268—9; evolution, xi, 455; 
in Ency. Brit., xi, 497—521.