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| Авторизация |
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| Casey J. — A treatise on the analytical geometry |
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| Предметный указатель |
Coordinates of point dividing in a given ratio the join of two given points 12 65
Coordinates of point of intersection of two lines given by a single equation 52
Coordinates of point of intersection of two lines whose equations are given 42
Coordinates of pole of line with respect to conic 338
Coordinates, a real of some important points 66
Coordinates, a real or barycentric 64
Coordinates, biangular or biradial 61
Coordinates, Cartesian 4
Coordinates, complementary and anticomplementary of a point 81
Coordinates, current 31
Coordinates, elliptic 233
Coordinates, normal of some important points 64
Coordinates, normal or trilinear 61
Coordinates, point and line, comparison of 86
Coordinates, polar 17
Coordinates, tangential or line 86
Coordinates, transformation of 19
Coordinates, tripolar or tricyclic 301
Covariant 462 477
Cremona 349
Crofton 136 239 244 279 284 322 344 528 530 531 533 536
Cubic, the seventeen point 460
Curtis, Prof S J 145 146 477 478 527 528 534
Curvature, centre of 185 186 216 264
Curvature, circle of 185 312
Curvature, radius of 185 186 216 264 313
Curve, Hermite 506 507
Curve, isoptic, of conic 520
Curves, pencils of 114
D'Ocagne 526 531
Dandelin and Quetelet 365
Darboux 111
De Longchamps 436 461 545
Desargues 521
Descartes 5
Determinant 40 41 74 SO
Determinant, of transformation 462
Diagonal points 71
Diagonal triangle 69
Diameters 155 179
Diameters, conjugate 157 534
Diameters, equation of pair of general conic 534
Diameters, equiconjugate 534
Diameters, through intersection of two tangents bisects chord of contact 108 212 261
Director circle 164
Directrix 173 201 223 250 311 510
Discriminant 51 334
Distance, between centres of two circles 107
Distance, between points of intersection of a given line with two given lines 79
Distance, between two points 6 78
Distance, of four points in plane, how connected 29
Distance, of point from vertices of triangle of reference 79
Double contact 318 320 513
Double contact, equation of two conics having double contact with a third 318
Double contact, equation to same 498
Double contact, lines and double points 285
Double contact, problem to describe one conic touching three others, each having double contact with a fourth 499
Double contact, properties of three conics having double contact with a fourth 319 320
Double contact, properties of two conics having double contact with a third 319
Eccentric angle 206
Eccentric angles of extremities of conjugate diameters 209
Eccentric angles, sum of, for feet of normals to ellipse 220
Eccentric angles, sum of, for four concyclic points on conic 241 280
Eccentricity 201 250
Eccentricity of any section of cone 366
Eccentricity of conic given by general equation 532
Eccentricity of hyperbola and conjugate, how related 279
ellipse 201—249
Ellipse, area of, given by general equation 331
Ellipse, axis of confocal 232
Ellipse, equation of tangent and normal to 208 214
Ellipse, equation of, referred to pair of conjugate diameters 211
Ellipse, equation of, referred to the equiconjugate diameters 212 279
Ellipse, evolute of 216
Ellipse, orthoptic circle of 224
Ellipse, parallel to 470
Ellipse, parallel to, reciprocal of 534
Ellipse, pedal of, with respect to centre, reciprocal polar of 228
Ellipse, pedal of, with respect to focus 221
Ellipse, polar equation of, with focus as pole 236
Ellipse, polar equations of tangent and normal to 237
Ellipse, Steiner's 362 421 451
Ellipse, the Brocard 391 403 411 420
Elliptic coordinates 233
Envelope of a system of confocal conics 347
Envelope of axis of perspective of a triangle circumscribed to one conic and its polar reciprocal with respect to another 479
Envelope of chord of conic subtending a right angle at a fixed point 358
Envelope of chord of conic subtending a right angle at focus 524
Envelope of chord of contact of tangents to a hyperbola from any point on conjugate hyperbola 262
Envelope of chords of osculation of para-bola 189
Envelope of line cutting a conic in points whose join subtends a right angle at origin 318
Envelope of line cutting three conics in involution 505
Envelope of line joining corresponding points on two lines divided homographically 385
Envelope of line joining extremities of conjugate diameters of ellipse 241
Envelope of line joining extremities of two perpendicular central vectors of ellipse 2—12
Envelope of line which cuts two conics harmonically 371
Envelope of line, if sum of squares of perpendiculars on it from any number of fixed points he constant 347
Envelope of line, the product of the perpendiculars on which from two fixed points is constant 221 266
Envelope of linos whose poles with respect to three conics are collinear 607
Envelope of polar of a given point with respect to a confocal system of conics 348
Envelope of the eight tangents to two conics at their points of intersection 490
Envelope of the polar of a given point with respect to any circum-conic of a quadrilateral 386
Envelope of the sides of Kiepert's triangles 458
Envelope of the six sides of two inscribed triangles of a conic 386
Envelope of third side of a triangle inscribed in a conic, two of whose sides touch another conic 348 529
Envelope of Tucker's circles 421
Envelope, Hermite, of a net of conics 506
Envelopes, theory of 346
Equation of asymptotes of conic given by general equation 166 465
Equation of axes of conic 159 519
Equation of bisectors of angles between two lines 53 54 465
Equation of bisectors of angles, of medians, and of perpendiculars of tri-angle of reference 62
Equation of Brocard line and diameter 67
Equation of circle circumscribed to triangle of reference 127 128
Equation of circle cutting three given circles at given angles 108
Equation of circle cutting three given circles orthogonally 109 149
Equation of circle inscribed in or described to triangle of reference 131
Equation of circle on join of two points as diameter 77 99 150
Equation of circle through three points 110 136
Equation of circles in pairs touching three given circles 120
Equation of conic confocal with a given conic and touching a given line 529
Equation of conic confocal with a given one 312 512
Equation of conic having double contact with two conics 318
Equation of conic having triangle of reference as autopolar triangle 337
Equation of conic referred to focus and directrix 338
Equation of conic referred to tangents and chord of contact 308
Equation of conic, given focus and three tangents 391
Equation of directrices of Brocard's ellipse 421
Equation of directrix of parabola 164
Equation of eight circles tangential to three given circles 109
Equation of Eiler's line 67
Equation of evolute 187 216 264
Equation of foci 322
Equation of four common tangents to two conics 488
Equation of four conics having double contact with a given conic and passing through three given points 522
Equation of four tangents to a conic at points of intersection by another conic 491
Equation of join of two points 40 66
Equation of join of two points on circle 102 130 133
Equation of join of two points on conic 176 208 270 338 342
Equation of line dividing angle between two lines into parts whose sines have a given ratio 46
Equation of line joining centre and synimedian point 67
Equation of line perpendicular to the given line 45 76
Equation of line through a given point making a given angle with a given line 44 45
Equation of line through, a given point parallel to a given line 70
Equation of lines equally inclined to bisectors of angles of triangle of reference 63
Equation of medians of triangle 41 62
Equation of normal 184 190 214 237 262 273
Equation of orthoptic circle of conic 164 224 341 510
Equation of perpendiculars of triangle 49 62
Equation of point pair in which a line intersects a conic 336
| Equation of polar of a given point 105 163
Equation of reciprocal of conic 387
Equation of six common chords of two conics 465
Equation of symmedian lines 63
Equation of tangent pair from point to curve 103 163
Equation of tangent to circle 101 130 134
Equation of tangent to conic 129 161 176 189 208 237 256 271 273 338 342
Equation of tangent to nine-point circle, at its point of contact with incircle 126
Equation of the cyclic points 75 88 509
Equation tangential 138 161 335
Equation, defined 33
Equation, general, of line or curve through the intersection of two lines or curves 39 40
Equation, general, of three concurrent lines 62
Equation, general, reduction to normal form 158
Equation, homogeneous represents lines through the origin 51
Equation, result of substituting coordinates of a point in 37 98 137
Fagnanis' theorem 227
Faure 524 526 541
Figures, complimentary and anticomplimentary 81
Figures, inversely similar 285 393 395
Focus 173 201 250 211 322 511 512 532
Focus of parabola touching four right lines 178
Fregier's theorem 227
Frobenius 111 495
Geometrical signification of the vanishing of a coefficient in general trilincar equation of the second degree 337
Gob 85
Graves, Dr. 311 322
Gugler 360"
Gundelfinger 473 490
hadamard 299
Hamilton law of force, proof of 232
Hamilton, Sir William 205 253
Harmonic chords, system of conics 482
Harmonic chords, theory of 406
Hart, Sir A. 132
Hermes 95
Hermite envelope of net of conics 506
Hervey 94
Hesse 32 516
Hexagon, harmonic 437
Hexagon, Lemoine 419
Homogeneous equations represent lines through the origin 51
Homographic division, theory of 368
Honiothetic figures 326
Hyperbola 251
Hyperbola, Apollonian 453 504 217 264
Hyperbola, conjugate 258
Hyperbola, conjugate, polar equation of 267
Hyperbola, coordinates of point on, expressed in terms of a single variable 245
Hyperbola, equation of asymptotes to 268
Hyperbola, equation of tangent and normal to 256 262 273
Hyperbola, equation of, referred to conjugate diameters 259
Hyperbola, equilateral 252
Hyperbola, equilateral, area of between asymptotes and two diameters 273
Hyperbola, equilateral, generation of 289
Hyperbola, equilateral, polar equation of 267
Hyperbola, Jcrabek's 448 449 483
Hyperbola, Kiepert's 431 442—445 449 452 453
Hyperbola, polar equation of, centre being pole 267
Hyperbola, polar equation of, focus as pole 272
Hyperbola, tangents at extremities of focal chord meet on directrix 277
Hyperbolas, Neuberg's 429 430 431 540
Hyperbolic functions 275
identities 520
Infinity, centre is pole of line at 167
Infinity, equation of line at 74
Infinity, every parabola touches line at 308
Intersection of line and conic 153
Intersection of two lines given by a single equation, coordinates of 52
Intersection of two lines, coordinates of 42
Invariant angles of two conics 471
Invariant, harmonic, of a system of conics 482
Invariant, orthogonal, of a system of conics 495
Invariant, tact, of product of six anharmonic ratios 4—72
Invariant, tact, of two conics 469
Invariants 159
Invariants, calculation of 467
Invariants, number of independent, &c, of two conics 517
Inverse points and lines 105
Inversion, of line or circle with respect to circle 105
Inversion, quantities unaltered by 113
Involution, central point of, double points of, hyperbolic, elliptic, symmetric, isogonal 378—380
Isogonal transformation 428
Jacobian 502 517
Jacoby 503
Jerabek 448
Joachimsthal 220. See also circle
Join of two points 8
Jonquiers, De 481
Kiehl 297 302
Koehler 484
Lachlan 111 114 138
Lagrange 27
Laguerre's theorem 219
Laisant 94 143
lame 172 233 405
Lame's equation 462
Latus rectum 160 174 203 252
Lemoine 144 418 529—531 544
Length of axes of conic given by general equation 330
Length of direct common tangent to two circles 100
Length of perpendicular from point to line 37 38 39 73
Length of perpendiculars from foci on tangent 220 265
Lhuilier's problem 359
Limiting points of a coaxal system 115 117
Line, Euler's 67 449
Line, Pascal's 328
Line, Simeon's 136
Lines, conjugate 106
Lines, double 285
Lines, four coneyclic 200
Lines, inverse 105
Lines, isotropic 75
Lines, symmedian 63 440
Locus of centre mean of feet of normals to a parabola 185
Locus of centre of Brocard ellipse, given base and Brocard angle 534
Locus of centre of circle harmonically circumscribed to parabola 521
Locus of centre of circle touching fixed line and circle 196
Locus of centre of circumcircle, given three tangents and sum of squares of axes 527
Locus of centre of conic harmonically inscribed in four conics 478
Locus of centre of conic inscribed in a quadrilateral 355 383
Locus of centre of conic through four points 171
Locus of centre of conic through three points, having an asymptote parallel to a given line 172
Locus of centre of conic touching four given lines 526
Locus of centre of curvature 187
Locus of centre of equilateral hyperbola described about a given triangle 266 290
Locus of centre of in conic through circum- and orthocentre 342
Locus of centre of reciprocation, when reciprocal conic is an equilateral hyperbola 386
Locus of centre, given a self-conjugate triangle and a tangent 533
Locus of double points of a given net of conics 501
Locus of double points of lines cutting three conics in involution 503
Locus of focus of variable conic, given tangent, one focus, and eccentricity 531
Locus of foot of perpendicular from focus on tangent 177 178 221 266
Locus of incentre given base and sum of sides 204
Locus of intersection of normals at extremities of a chord passing through a given point 188 466
Locus of intersection of tangents at extremities of a pair of conjugate diameters 241
Locus of intersection of tangents at two points, whose join subtends a given angle at focus 524
Locus of middle points of a system of parallel chords of a conic 155 156 179 255 208
Locus of middle points of chords of ellipse passing through a given point 239
Locus of middle points of chords of parabola subtending a right angle at the vertex 196
Locus of middle points of variable chords of a circle subtending a right angle at a given point 101
Locus of orthocentre, given base and vertical angle 99
Locus of point the area of whose pedal triangle is given 135 297
Locus of point the chord of contact of tangents from which to a given circle subtends a light angle at a given point 104
Locus of point whence sum of tangents to two circles is given 239
Locus of point whence tangents to conic contain a given angle 184 520
Locus of point whence tangents to three conics form a pencil in involution 507
Locus of point whence tangents to two confocals are at right angles 225
Locus of point where parallel chords of a conic are cut in a given ratio 355
Locus of point whose pedal i angle has a constant Brocard angle 300
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