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| Casey J. — A treatise on the analytical geometry |
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| Предметный указатель |
Locus of point whose polars with respect to three conics are concurrent 502
Locus of point whose polars with, respect to two circles meet on a given line 526
Locus of point, fixed in line of given length sliding between two fixed rectangular lines 205 213
Locus of points having the same eccentric angle on a system of con-focal ellipses 236
Locus of points of contact of parallel tangents to a system of con-focal ellipses 236
Locus of points on a system of confocal conics, the osculating circle at which passes through a focus 331
Locus of points the sum of the squares of the sides of whose pedal triangles is given 300
Locus of points whence tangents to two conics form an harmonic pencil 370 477
Locus of pole of a chord of a conic sub-tending a right angle at a given point 175 277
Locus of pole of chord of equilateral hyperbola such that the osculating circle at one extremity passes through the other 284
Locus of pole of Hue with respect to an income satisfying any condition 339
Locus of pole of line with respect to a confocal system 236
Locus of pole of variable chord passing through a given point 341
Locus of polo of normals to ellipse 241
Locus of symmedian point, given base and area 525
Locus of symmedian point, given base and vertical angle 331
Locus of vertex of a circum polygon a conic when all the other vertices move on confocal coni 324
Locus of vertex of a given triangle whose two other angular points move on two fixed lines 213
Locus of vertex of a triangle circum scribed to one conic, two whose angular points move another conic 486
Locus of vertex of a variable triangle, whose sides pass through fix points, and whose base angle move on fixed lines 376
Locus of vertex of all right cones out which a given ellipse can cut 367
Locus of vertex of triangle self-conjugate with respect to one con two of whose vertices lie another conic 527
Locus of vertex, given base a Brocard angle 423
Locus of vertex, given base and difference of sides, or difference of base angles 252
Locus of vertex, given base and sum of sides, or product of tangents of base angles 204
Locus of vertex, given base and vertical angle 99
Lucas 283 304 306
M'Cay 96 247 332 403 404 447 459 525
M'Cay's extension of Feurbactts theorem 329
M'Cullagh 242 243 324 362
Maclaurin's method of generating conics 376
Malet's theorem 317
Malet, J.C. 471
Mandart 461 544
Mannheim 211 220
Mathesis 306 429 441
Mathieu 68
Minors 52
Modular quadrangle 0
Modulus 24 137
Negative 1 5
Neuberg 28 29 50 90 91 93 143 144 150 198 200 300 301 302 303 314 360 361 363 367 398 401 404 423 429 441 460 401 519 531 533 537 538 539 540 543
Neuberg and Gob 458 459
Neuberg and Schoute 300 537
Newton's method of generating conics 2
Newton's Theorem 167
Newtonian of quadrilateral 91
Nine-point circle 125 126 144 302 434 435 444 445
Nine-point conic 171
Norm 121 122 139
normal 184 214 262
Normal, polar equation of 190 237 273
Normal, sub 184
Normals, feet of, from any point to parabola lie on circle 185
Normals, feet of, to ellipse or hyperbola lie on hyperbola 216 264
Normals, four can be drawn to ellipse or hyperbola 216 264
Normals, Number of conditions to determine a conic 170
Normals, of independent invariants, &c, of two conics 517
Normals, three can be drawn from any point to parabola 184
Ordinates 4
Origin 1 5
Origin, change of 152
Orthocentre lies on circumscribing equilateral hyperbola 290
Orthocentre of triangle formed by three tangents to a parabola 172
Orthocentre of triangle is a point on directrix 178
Orthocentre, coordinates of 64 66
Orthocentre, join of to centroid 67 77
Orthogonal conics 495 497 499 501 502
Orthogonal invariant of two conics 495
Orthogonal projection of circle 206
Orthogonal system of circles 107 109 110 117 118
Orthologique triangles 50
Osculating circle 185 309 310
Osculating circles, six of given conic can be described to cut a given circle orthogonally 316
Osculating circles, six of given conic can be described to cut a given circle orthogonally and their centres lie on a conic 317
Osculating conic of a given circum conic 310
Osculation 309 471
Osculation, chord of 313
Osculation, four chords of through any point in plane of conic 314
Osculation, hyper 318 321
Parabelae, Artzt's 441 483
Parabelae, Artzt's directrices of 442
Parabelae, Brocard 439
parabola 154 157—160 169 173—200
Parabola, a tangential equation of 198
Parabola, axis of 158 159
Parabola, centre of 154
Parabola, coordinates of origin in 160
Parabola, directrix of 164
Parabola, every, touches line at infinity 368
Parabola, is first negative pedal of right line 178
Parabola, Kinpert's 458
Parabola, parameter of 115 1G0 203
Parabola, pedal of, with respect to focus 178
Parabola, polar equation of, focus being pole 189
Parabola, Purser's 220
Parabola, referred to any diameter and tangent 182
Parabola, subnormal in constant 184
Pascal's theorem 145 328
Pascal's theorem proved by projection 354
Pascal's theorem, reciprocal of 385
Pedal and antipedal triangles 296
Pedal and antipedal triangles, area of 297
Pedals, positive and negative 177 221 266 416
Pencil of conics 463
Pencil of lines when harmonic 59
Pencils, inversely equal 288
Perpendicular, length of from point to line 37 73
Perpendiculars of triangle are concurrent 62
Perspective, axis of, is trilinear polar of centre of 130
Perspective, triangle of reference and that formed by tangents to circum conic at vertices are in 129
Perspective, triangles in multiple 82
Perspective, triangles in, axis and centre of 72
Pluecker 540
Pohlke 205
Point, director 399
Point, power of 37
Point, Steiner's 133
Point, Tarry's 446 452
Points, adjoint 399
Points, Brocard 64
Points, complimentary and anticomplimentary 81
Points, conjugate 106
Points, coordinates of a few important 64 66
Points, cyclic 75 88
Points, diagonal 71
Points, distance between two 6 78
Points, double 285 376 393
Points, double, found geometrically 377
Points, harmonic system of 56
Points, invariable 397
Points, inverse 105
Points, isobaryc group of 85
Points, isodynamic 303
Points, limiting, of conxal system 115
Points, Nagel's and Gergonne 95 133 394 409 461
Points, symmedian 407 438 456
| Points, twin 292
Points, twin, are isogonal conjugates of inverse points with, respect to circle 293
Points, which correspond to infinity 373
Polar coordinates 17
Polar reciprocal of curve 228
Polar reciprocal of one conic with respect to another 480
Pole and polar of circle 105
Pole and polar trilinear 68
Pole normal 218
Poles and Mars 163
Poncelet 221 484 539
Positive 5
Projection 3 349
Projection of a system of coaxal circles 352
Projection of a system of concentric circles 351
Projection orthogonal 358
Projection orthogonal of circle 206
Projective properties 351
Projective properties, pencils 374
Projective properties, rows 371
Ptolemy's theorem, extension of 329
Purser's parabola 220
Purser, F.R.U.I. 248 249 331 357
Purser, F.T.C.D. 199 200 220 315 331 526 533
Quadrangle complete and standard 69 70
Quadrangle complete and standard, pencil of 391
Quadrangles, metapolar and metapole of 392
Quadrangles, modular 397
Quadrilateral complete 69
Quadrilateral complete, each diagonal of divided harmonically by other two 70
Quadrilateral, harmonically diagonal points and triangle of 69
Quadrilateral, harmonically middle points of three diagonals collinear 43
Quadrilateral, harmonically Newtonian of 91
Quadrilateral, standard 70
Radical axis and centre 115 117
Radius vector 17
Radius vector of circle given by general equation 97
Radius vector of circle of coaxal system 115
Radius vector of curvature 185 186 216 264 313
Radius vector of curvature of conic at origin 310
Ratio of section 55
Reciprocal polars 384
Reciprocal polars, some theorems proved by 385
Reciprocation, centre of 386
Reciprocation, centre of, that polar reciprocal of a given triangle may be similar to another triangle 388
Reduction of conic to centre 155
Reduction of general equation of line to standard form 35
Relation between area of triangle, lengths of its sides, and normal coordinates of any point in its plane 62
Relation between baryecntric coordinates of isotomic points 65
Relation between Brocard and Steiner angles 459
Relation between coefficients of general equation when it represents a circle 134
Relation between eccentric angles of two points whose join passes through focus 222 277
Relation between normal coordinates of isogonal conjugate points 63between normal and barycentric
Relation between tripolar and normal coordinates 303
Relation coordinatos of a point 65
Relation identical connecting any four lines no three of which are concurrent 70
Relations, identical 513
Relations, three special, which a triangle can have with respect to a conic 468
Ritchie 190 191
Roberts, M. 236
Roberts, R.A. 196 197 246 283 318 332
Rule of signs 1
Salmon 68 70 321 333 344 371 465 473 477 479 487 530 532
Schooten 213
Schoute, circles 300 403
Schroeeter 535
Self-conjugate or autopolar triangle 337 468 491
Serret, P. 522
Similar conics 326
Similar conics, conics have equal eccentricity 327
Similar conics, rows 373
Similitude, centre and circle of 118 119
Similitude, six centres of, for any three circles lie three by three on four right lines 119
Simmons 538
Smith, H.J.S. 475 481
Sollertinsky 512
Staudt 114 371 477
Steiner 17 37 50 69 147 239 315 329 528
Stewart's theorem (Sequel) 304
Sum of eccentric angles of four con-cyclic points on conic 241 280
Sum of reciprocals of segments of focal chords of ellipse 237
Sum of reciprocals of two chords of ellipse at right angles and touching confocal 248
Sum of squares of two conjugate semi-diameters of ellipse 209
Supplemental chords 213
Sylvester 503
Symmedian lines 414 440
Symmedian point 63 407 413 418
Tact invariant of two conics 469
Tangent 161
Tangent at infinity 166
Tangent to circle 101 130 134
Tangent to conic 161
Tangent to nine-points circle at point of contact with incircle 126
Tangent, sub, bisected at vertex in parabola 177
Tangential circles, a system of 120
Tangential circles, equation of all conics confocal with a given one 312 511
Tangential circles, equation of centre of conic 344
Tangential circles, equation of circle circumscribed to triangle of reference 138
Tangential circles, equation of circle inscribed in triangle of reference 140
Tangential circles, equation of circle referred to two tangents and chord of contact 344
Tangential circles, equation of circle, given radius and centre 143
Tangential circles, equation of conic 161 344
Tangential circles, equation of conic given a focus and circum triangle 390
Tangential circles, equation of conic having triangle of reference as self-conjugate triangle 341
Tangential circles, equation of cyclic points 75 508
Tangential circles, equation of envelope of line cut in involution by three conics 505
Tangential circles, equation of four points common to two conics 489
Tangential circles, equation of hyperbola 261
Tangential circles, equation of parabola 198
Tangential circles, equations 161 335
Tangential circles, pencil and net of conics 463
Tarry 395 397 418
Tesch 538
Townsend 218 325 345 370 381
Transformation of coordinates, determinant of 462
Transformation of coordinates, harmonic, area of 299
Transformation of coordinates, harmonic, of triangle 298
Transformation of coordinates, isogonal 428
Transformation of coordinates, of general conic 152 155
Triangle of similitude 395
Triangle, diagonal 69
Triangle, invariable 397
Triangle, Kiepert's 443
Triangles, annex 399 468 491
Triangles, autopolar or self-conjugate 337
Triangles, circum vertices of two lie on a conic 386
Triangles, first and second, of Brocard 422
Triangles, formed by three points and their three polars with respect to any conic are in perspective 340
Triangles, inscribed sides of touch a conic 386
Triangles, Lionnet's 389 401 403 404
Triangles, orthologique 50
Triangles, pedal and antipodal 296
Tucker 441
Value of k so that  may be an equilateral hyperbola 171
Variables 31
Variables, complex 21
Whewell 177
Wright 149
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