# A Treatise on Conic Sections

American Mathematical Soc., 2005 - Mathematics - 399 pages
The classic book on the subject, covering the whole ground and full of touches of genius.

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### Contents

 CHAPTER 1 Polar Coordinates 10 Meaning of the Constants in Equation of a Right Line 17 Equation of Line joining two given Points 23 Length of Perpendicular from a Point on a Line 28 Test that three Equations may represent Right Lines meeting in a Point 34 Loci solved by Polar Coordinates 51 Algebraic Expression for Anharmonic Ratio of a Pencil 57
 Polar Equation of Parabola 207 Radii Vectores through Foci have equal difference of Reciprocals 212 Similar Conic Sections 222 CHAPTER XIV 232 Equation of Conic passing through five given Points 233 Form of Equation referred to a selfconjugate Triangle see also p 253 239 Pascals Theorem see also pp 280 301 316 319 379 246 Selfconjugate Triangle common to two Conies see also pp 348 361 256

 Intersections of Perpendiculars of Bisectors of Sides and of Perpendiculars 63 Meaning of an Equation resolvable into Factors 67 Number of conditions that higher Equations may represent Eight Lines 74 Equation of Tangent to a Circle at a given Point 80 80 Circle through three Points see also p 130 86 Conjugate Triangles Homologous 92 Equation of radical Axis of two Circle3 99 Centres of Similitude 105 To describe a Circle touching three given Circles see also pp 115 135 291 113 Locus of Point such that Area of Triangle formed by feet of Perpendiculars 119 Equation of inscribed Circle derived from that of circumscribing 125 Condition that four Circles may have a common orthogonal Circle 131 Transformation to Parallel Axes of Equation of second Degree 137 Discussion of Quadratic which determines Points where Line meets a Conic 183 139 Diameters of Parabola meet Curve at infinity 145 Analytic condition that four Points should form a Harmonic System 305 146 Case where one of the Lines meets the Curve at infinity 151 Functions of the Coefficients which are unaltered by transformation 157 Figure of Hyperbola 163 Locus of intersection of Normals at extremities of a Focal Chord see also p 335 211 166 Length of central Perpendicular on Tangent 169 To draw a Normal through a given Point see also p 335 174 Rectangle under Focal Perpendiculars on Tangent is constant 180 Origin of names Parabola Hyperbola and Ellipse see also p 328 186 Lines joining two fixed to variable Point make constant Intercept on Asymptote 192 Parabola the limit of the Ellipse when one Focus passes to infinity 200
 Discriminant of Tangential Equation 262 Equation of pair of Tangents through a given Point see also p 149 269 To inscribe in a Conic a Triangle whose sides pass through fixed Points see 273 Principle of Duality 276 Locus of Focus given four Tangents see also p 277 277 Polar of one Circle with regard to another 283 Carnots Theorem respecting Triangle cut by Conic see also p 319 290 Centre the Pole of the line at infinity 296 Generalizations of MacLaurins Method of generating Conies see also p 300 251 300 Criterion whether two Systems of Points be Homographic see also p 383 304 Condition that Line should be cut Harmonically by two Conies 306 System of Conies touching four Lines when cut a Transversal in Involution 313 Projective proof of Camots Theorem see also p 289 319 Sections of a Cone 326 Orthogonal Projection 332 Criterion whether Conies intersect in two real and two imaginary Points or not 337 Tangential equation of four Points common to two Conies 343 Envelope of Base of Triangle inscribed in one Conic two of whose sides touch 349 Equation of reciprocal of two Conies having double contact 356 To form the equation of the sides of selfconjugate Triangle common to 362 Three Conies derived from a single Cubic method of forming its Equation 368 Line which cuts off from a Curve constant Arc or which is of a constant length 374 Theorems on complete Figure formed by six Points on a Conic 879 383 On systems of Conies satisfying four Conditions 38S 391 Copyright