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Название: A treatise on the analytical geometry

Автор: Casey J.

Язык: 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 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 should be antiparallel to 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 and 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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