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Casey J. — A treatise on the analytical geometry
Casey J. — A treatise on the analytical geometry



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Название: A treatise on the analytical geometry

Автор: Casey J.

Язык: en

Рубрика: Математика/Геометрия и топология/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: second edition

Количество страниц: 564

Добавлена в каталог: 18.11.2004

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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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