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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

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Abscissae      4
Allersma      218
Andre Desire      28
Angle between asymptotes      166 268
Angle between central vector to, and normal at, a point on ellipse      244
Angle between focal radius vector and tangent      221
Angle between focal vectors bisected by tangent and normal      221
Angle between tangents to a parabola in terms of their lengths and chord of contact      191
Angle between two lines given by a single equation      53
Angle between two lines whose cartesian equations are given      36 37
Angle between two lines whose cartesian equations are given, same for trilinear equations      73
Angle between two tangents to an ellipse      224 234
Angle between two tangents to an ellipse, same expressed in terms of focal vectors to points of intersection      225
Angle of intersection of two circles or curves      107
Angle of intersection of two parabolas      199
Angle, eccentric      206
Angle, first and second, of Steiner      426
Angle, intrinsic      175 177
Angle, intrinsic, same half polar angle of point on parabola      191
Angle, subtended at focus by portion of variable tangent intercepted by two fixed tangents      238
Angle, the Brocard      64 409 411 459
Angles, eccentric, of extremities of conjugate diameters how related      209
Angles, sum of for four concyclic points on conic      241 280
Angles, theorems concerning, how projected      353
Anharmonic ratio of double points and homologous point pairs      376
Anharmonic ratio of four collinear points      55 163
Anharmonic ratio of four conics of a pencil of conics, six of four points      59
Anharmonic ratio of four eollinear points equal to that of pencil formed by their four polars      106
Anharmonic ratio of four lines whose equations are given      59
Anharmonic ratio of four points in which tangent at any variable point meets tangents at four fixed points on conic      344
Anharmonic ratio of four rays of a pencil      57
Anharmonic ratio of four tangents to a conic      385
Anharmonic ratio of pencil formed by two legs of an angle and the isotropic lines of vertex      353
Anharmonic ratio of pencil from any point of conic through four fixed points, to the four points      473
Anharmonic ratio of pencil from variable point to four fixed points on conic      343
Anharmonic ratio of pencil same as that of the four points in which any transversal is cut by rays      58
Anharmonic ratio of pencil unaltered by projection      351
Anharmonic ratio of points in two projective rows      372
Anharmonic ratio of rays in two projective pencils      375
Anharmonic ratio same expressed by trigonometrical ratios      60
Anomaly eccentric      206
Anomaly true      189 236
Antifoci      311 512
Antiparallel      77
Apollonius, circles of      146
Apollonius, first and second theorems of      210
Arcs of conics, theorems concerning      322 323 324
Area of hyperbola and hyperbolic sector      273—275
Area of parabolic sector      199
Area of parallelogram circumscribed to ellipse      210
Area of parallelogram formed by asymptotes and parallels to* them through any point on curve      269
Area of triangle formed by a given line, and a given line pair      80
Area of triangle formed by asymptotes and any tangent      271
Area of triangle formed by asymptotes and normal at any point on an equilateral hyperbola      282
Area of triangle formed by focus and two points on parabola      196
Area of triangle formed by joining extremities of conjugate semi-diameters      210 259
Area of triangle formed by three lines whose equations are given      81
Area of triangle formed by three points in tripolar coordinates      306
Area of triangle formed by three points on a conic      11 12
Area of triangle formed by three points on, or three tangents to, an equilateral hyperbola      283
Area of triangle formed by three tangents to a parabola half that formed by points of contact      179
Area of triangle formed by three tangents to hyperbola      271
Area of triangle formed by two tangents and chord of contact      104 106 240
Area of triangle or polygon in terms of coordinates of vertices      10 79
Area of triangle self-conjugate with respect to, inscribed in, or circumscribed to, a conic      243
Area of triangle which is the harmonic transformation of a given triangle      299
Area of triangle which is the pedal triangle of a given point      297
Area of triangle which is the polar reciprocal of a given triangle      299
Area, conic given by general equation      331
Areas, signs of      2
Argument      24
Aronhold's notation      333
Artzt      292 537
Asymptotes are self-conjugate      167
Asymptotes equation of, for hyperbola      268 279
Asymptotes of conic given by general equation      166 465
Asymptotes of equilateral hyperbola are at right angles      106 268
Asymptotes, chord of contact of      167
Asymptotes, constant length intercepted on, by joins of variable to two fixed points on cuivc      271
Asymptotes, defined      166
Asymptotes, divided homographically by parallels to from a series of points on curve      280
Asymptotes, equal intercepts on any chord between curve and      270
Asymptotes, equation of, differs from equation to curve by a constant      268
Asymptotes, hyperbola referred to, as axes      167 269
Asymptotes, intersect in centre      167
Asymptotes, lines joining extremities of any diameter to extremities of conjugate are parallel to      268
Asymptotes, points of intersection of any tangent with, and two foci are con cyclic      281
Asymptotes, polar of any point on either is parallel to that one      281
Asymptotes, secant of half angle between, gives eccentricity      268
Axes of conic given by general equation      519
Axes of conics      158
Axes of conics confocal with a given one, and passing through a given point      232 233
Axes of parabola      158 159
Axes of perspective      72 130
Axes of similitude      119
Axes, are parallel to a pair of conjugate diameters of conic in whose equation coefficient of xy vanishes      157
Axes, lengths of, for conic given by general equation      330
Axes, magnitude and direction of, given two conjugate diameters of conic      210 271
Axes, radical      115
Axes, radical, of three circles are concurrent      116
Axes, rectangular and oblique      4
Axes, transverse and conjugate      203
Bisectors of angles between lines given by a single equation      53 54 465
Bisectors of sides or angles of a triangle are concurrent      62
Boscovich, method of generating conics      205 253
Brianchon's theorem      147 319
Briot and Bouquet      21
Brocard      166 174 179 195 198 441 459
Burnside      225
Catncart      510
Cayley      468 499 539
Centre of circle      97
Centre of circle, cutting three circles orthogonally      117
Centre of conic      153 154 203 251
Centre of curvature      185 186 216 264
Centre of incircle, in terms of coordinates of vertices and lengths of sides      16
Centre of inversion      408 411
Centre of involution      379
Centre of parabola      154
Centre of perspective      72 130
Centre of reciprocation      385
Centre of similitude      118 393
Centre of similitude, six of three circles, lie three by three on four right lines      119
Centre recherche of      154
Centre reduction of general equation to      155
Centre, line of centres      155
Centre, pole of line at infinity      167
Centre, radical      117
Centre, theory of mean      14—16
Chasles      219 225 235 324 343
Chord of conic which touches confocal, proportional to square of parallel semi diameter      225
Chord of contact of two tangents to a conic      183 223 256
Chord, joining two points on circle      102 130 133
Chord, joining two points on conic      175 208
Chord, locus of pole of, subtending a right angle at a fixed point      104 195 277
Chord, through a focus      183 222 277
Chords of contact of common tangents to two circles      103
Chords of intersection of two conics      213
Chords, conjugate      158
Chords, locus of middle points of parallel      155 156 179 208 255
Chords, supplemental      213
Circle director      164
Circle of curvature      185 312
Circle of inversion      104
Circle of reciprocation      386
Circle of similitude      119 395
Circle through 3 points      110 111 136
Circle through feet of perpendiculars      144
Circle touching three others      110 111 121
Circle, auxiliary      206 266
Circle, Boscovich      205
Circle, Brocard      408 411 422 524
Circle, centre of      117
Circle, circum, in barycentric coordinates      131
Circle, circum, is polar conic of symmedian point      127
Circle, circum, of polygon      129
Circle, circum, of triangle formed by three tangents to a parabola, passes through focus      178 190
Circle, circum, of triangle of reference      128
Circle, circumscribed to quadrilateral      143
Circle, cutting three given circles at given angles, or orthogonally      108 149
Circle, diameter of, cutting three given circles orthogonally      148
Circle, Dr. Hart's      147
Circle, equation of      96 108—111
Circle, equation of tangents from any point to      103
Circle, equation of, on join of two points as diameter      77 150
Circle, equation of, referred to two tangents and chord of contact      143 342
Circle, focal      311
Circle, geometrical representation of power of point with respect to      98
Circle, having as diameter chord of contact of tangents to a given circle from a given point      102
Circle, having as diameter the intercept made by a given circle on a given line      100
Circle, having side of triangle of reference as diameter      144
Circle, having triangle of reference as autopolar triangle      339
Circle, inscribed in triangle of reference      131
Circle, Joachimsthal's      185 187 188 218 264
Circle, Lemoine      419
Circle, Lionnets      401
Circle, nine-points      125 126 147 303 434 435 444 445 451 454
Circle, nine-points, touches both in- and ex-circles      125 138 149
Circle, orthocentroidal      436
Circle, orthogonal projection of      206
Circle, orthoptic      164 509 510
Circle, osculating      189
Circle, pedal of a given point      137
Circle, Steiner's      315
Circle, tangential equation of      138 139 140 141 143
Circles of Apollonius      146
Circles, a system of tangential      120
Circles, all pass through cyclic points      303
Circles, annex      401
Circles, coaxal system of      114
Circles, concentric, have double contact at infinity      328
Circles, concentric, when      97
Circles, described to triangle of reference      132
Circles, equation of, in pairs, touching three given circles      120
Circles, Fuhrman's      431
Circles, M'Cay's      427 454
Circles, Mutual power of two      107 108
Circles, Neuberg's      423—427 443 444 452 459
Circles, Tucker's      415 419 421
Clehsch      333 337 462
Coates' theorem      68 93 127
Complex variables      24
Concomitant, mixed      463 517
Condition that $l\alpha+m\beta+n\gamma=0$ should be antiparallel to $\gamma=0$      77
Condition that a circle may be cut orthogonally by four given circles      110
Condition that a line may he cut harmonically by two conics      371
Condition that a line should be cut in involution by three conics      505
Condition that a line should be perpendicular to itself      76
Condition that a line should cut a conic in two points which subtend a right angle at the origin      348
Condition that a line should pass through a given point      86 89
Condition that a line should pass through origin      33
Condition that a line should touch a conic      161 163 261 335
Condition that a triangle may be circum-scribed to one conic and hare its vertices on three other conics      485
Condition that a triangle may be inscribed in one conic, and have its sides touching three other conics      484
Condition that a triangle self-conjugate with respect to one conic may be inscribed in, or circumscribed to, another      475
Condition that any number of circles may have one common tangential circle      122
Condition that four circles should cut a fifth orthogonally or be tangential to it      112
Condition that four conics should cut a fifth orthogonally or be tangential to it      497
Condition that four convergent rays should form a harmonic pencil      59
Condition that four points on conic should be concyclic      241 280
Condition that four points should be concyclic      110
Condition that general equation should represent a circle (in Cartesian coordinates)      96
Condition that general equation should represent a circle in barycentric coordinates      137
Condition that general equation should represent a circle in normal coordinates      134
Condition that general equation should represent an ellipse, a parabola, or hyperbola      340
Condition that general equation should represent an equilateral hyperbola or a parabola      509
Condition that general equation should represent two right lines      51 52 334
Condition that intercept made by circle on line should subtend a right angle at a fixed point      100
Condition that joins of vertices of triangle of reference to points in which general conic meets sides should form two concurrent triads      527
Condition that normals at three points on ellipse, should be concurrent      215
Condition that normals at three points on parabola should be concurrent      188
Condition that three conics may have a common point      517
Condition that three lines should he concurrent      48
Condition that three points may be collinear      8
Condition that three-point pairs should form an involution      379
Condition that triangle of reference may be in perspective with one the coordinates of whose vertices are given      82
Condition that two circles should be concentric      97
Condition that two circles should cut orthogonally      107
Condition that two circles should touch      107
Condition that two conics are so related that a triangle may be inscribed in one and circumscribed to the other      468
Condition that two conics inscribed in the same conic should cut orthogonally      495
Condition that two conics should be homothetic      326 327
Condition that two conics should touch, osculate      309 469 471
Condition that two lines should be parallel      36 74
Condition that two lines should he at right angles      36 37 53 74
Condition that two lines should intersect on a conic      336 520
Condition that two points may be conjugate with respect to a conic      334
Condition that two points may be conjugate with respect to two lines      336
Condition that two-point pairs should be harmonic conjugates      57 368
Condition that when general equation represents two lines they should be parallel or perpendicular      77
Cone, right and oblique, sections of      363
Confocal conics      224—227 232—236 239 247 248 279 311 324 331 332
Confocal conics are inscribed in the same imaginary quadrilateral      311
Confocal conics, cut at right angles      333
Confocal conics, general equation of      312 512
Confocal conics, length, of are intercepted between tangents from      322—324
Conic through, five points, description of      172
Conic, eight points of contact of common tangents to two conics lie on a      488
Conic, equation of, given focus and three tangents      391
Conic, fourteen-line      490
Conic, fourteen-point      487
Conic, isoptic curve of      184 520
Conic, isotomic transformation of      296
Conic, nine-point of quadrangle      165
Conic, number of conditions sufficient to determine a      170
Conic, polar conic of point, and pole of      27
Conic, which reciprocates the Brocard ellipse into Kiepert's hyperbola      509
Conics, classification of      165
Conics, conjugate with respect to quadrilateral      514
Conics, diametral      445
Conics, for which $\Theta_1$ and $\Theta_2$ vanish      482
Conics, harmonic properties of      479
Conics, harmonic system of      482
Conics, homothetic      326
Conics, invariant angles of two      471
Conics, invariant theory of      462
Conics, mutual power of two      493
Conics, orthogonal      499
Conics, osculation of two      471
Conics, pencil and net of, tangential and trilinear      463
Conics, point and line harmonic conics of two      371
Conjugate area of triangle included by      210 259
Conjugate diameters      157 258
Conjugate diameters are parallel to a pair of supplemental chords      213
Conjugate diameters, equation of conic referred to as axes      211 259
Conjugate eccentric angles of extremities of      209
Conjugate hyperbola      257
Conjugate points and lines      106 334 336
Conjugate sum of squares of      209
Conjugates, harmonic      13 56 117 368 369
Conjugates, isogonal      63
Conjugates, isotomic      13 65
Constants      31
Contact, double      318 513
Contact, four-pointic      318 321
Contact, of different orders      309
Contravariants      508
Coordinates of double points      334
Coordinates of incentre of triangle in terms of coordinates of vertices and lengths of sides      16
Coordinates of orthocentre of triangle formed by tangents to ellipse and chord of contact      245
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