A Treatise on Conic Sections

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American Mathematical Soc., 2005 - Mathematics - 399 pages
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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
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