Locus of, such that Emr2 = constant, 88. cutting in given anharmonic ratio, on perpendicular at height from base such that triangle formed by joining 298. on line cut in given anharmonic ratio, chords through which subtend right! whose polars with respect to three of parallel chords of conic, 143. of convergent chords of circle, 96. 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 271. intersection of tangents to a conic 269, 352. 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- focus of parabola given three tan- MacCullagh, theorems by, 210, 220, 333, 374, 377. Mac Laurin's mode of generating conics, Middle points of diagonals of quadrilate- Moore, deduction of Steiner's theorem from 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. Pappus, 186, 295, 328. Parabola (see Contents, pp. 195–207, 212-214). origin of name, 180, 328. has tangent at infinity, 235, 290, 329. Parallel to conic, equation of, 337. same for reciprocals of equal circles, Pascal's hexagon, 245, 280, 301, 319, 380. Perpendicular, equation and length, 26, 60. extension of relation, 321, 354. from centre and foci on tangent, 169, middle points of diagonals lie on diagonals of inscribed and circum- scribed form harmonic pencil, 242. Radical axis and centre, 99, 122, 224, 282. Reciprocals, method of, 66, 276, 294, 356. Sadleir, theorems by, 184. Self-conjugate triangles, 91. Similar conics, 222. condition for 224. have points common at infinity, 236. Steiner, theorem on triangle circumscribing Systems of circles having common radical of conics through four points cut a Tangent, general definition of, 78. to conic constructed geometrically, 151. Tangential equations, 65, 276, &c., 383, 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. 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