Locus of, such that Emr2 = constant, 88. cutting in given anharmonic ratio, on perpendicular at height from base such that triangle formed by joining on line cut in given anharmonic ratio, of which other three describe right chords through which subtend right whose polars with respect to three of parallel chords of conic, 143. 51. of perpendicular on tangent from focal radius vector with corresponding of perpendiculars to sides at extremity of perpendiculars of triangle given base of perpendiculars of triangle inscribed eccentric vector with corresponding polars with respect to fixed conics of to a parabola which cut at given at extremities of conjugate dia- meters, 209. whose chord subtends constant angle from two points, which cut a given each or both on one of four given Locus of, at two fixed points on a conic satisfy- or chord through fixed point, 214, 335. on normal of parabola. 213. centre of inscribed circle given base of circle cutting three at equal angles, of circumscribing circle given vertical of circle touching two given circles, centre of conic (or pole of fixed line) given four points, 153, 254, 268, given four tangents, 216, 254, 267, given three tangents and sum of four conditions, 267, 389. pole of fixed line with regard to sys- pole with respect to one conic of tan- mon to fixed conic, and variable of Mac Cullagh, theorems by, 210, 220, 333, 374, 377. Mac Laurin's mode of generating conics, Brianchon's, 247. Mulcahy, on angles subtended at focus, 331. Number of terms in general equation, 74. of conditions to determine a conic, 136. Number of concomitants to system of | Self-conjugate triangle conics, 363. O'Brien, 217. Orthogonal systems of circles, 102, 131, Osculating circle, 227, 234. vertices of two lie on a conic, 322, 341. Serret on locus of centre given four three pass through given point on Similitude, centre of, 105, 223, 282. curve, 229. origin of name, 180, 328. has tangent at infinity, 235, 290, 329. coordinates of focus, 239, 274, 354. Parallel to conic, equation of, 337. same for reciprocals of equal circles, Perpendicular, equation and length, 26, 60. extension of relation, 321, 354. from centre and foci on tangent, 169, Pliicker, 278, 380. Polar coordinates and equations, 9, 36, poles and polars, properties of, 92, 148. point and polar equivalent to two Quadrilateral, middle points of diagonals lie on diagonals of inscribed and circum- scribed form harmonic pencil, 242. Radical axis and centre, 99, 122, 224, 282. Sadleir, theorems by, 184. Self-conjugate triangles, 91. Similar conics, 222. condition for 224. have points common at infinity, 236. of inscribed and circumscribing circles, of circle in general, 128, 384. of conic in general, 152, 260. of points common to four conics, 344. Townsend, theorems and proofs by, 252, Transformation of coordinates, 6, 9, 157, Transversal, how cuts sides of triangle, 35. Triangle, circumscribing, vertices or two Triangles made by four lines, properties Trilinear coordinates, 57, 60, 264. Veronese, 382. circle having triangle of reference for, Walker, 391. BY THE SAME AUTHOR. A TREATISE ON THE HIGHER PLANE CURVES. Third Edition. Dublin: HODGES, FOSTER, AND FIGGIS. 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