A Treatise on Conic Sections: Containing an Account of Some of the Most Important Modern Algebraic and Geometric Methods

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Longmans, Green, and Company, 1879 - 399 pàgines
 

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Middle Points of Diagonals of a Quadrilateral are in a Right Line see also p
62
RIGHT LINES
67
Number of conditions that higher Equations may represent Right Lines
74
Equation of Tangent to a Circle at a given Point 80
80
Equation of Perpendicular on a given Line
81
Circle through three Points see also p 130
86
Conjugate Triangles Homologous
92
PROPERTIES OF TWO OR MORE CIRCLES
98
its Properties
99
Centres of Similitude
105
To describe a Circle touching three given Circles see also pp 115 135 291
111
THE CIRCLEABRIDGED NOTATION
117
Its Tangential Equation
124
Determinant Expressions for Area of Triangle formed by three Lines
130
Equation of Conic passing through five given Points
134
CHAPTER X
136
Discussion of Quadratic which determines Points where Line meets a Conic 188
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
Intersections of Perpendiculars of Bisectors of Sides and of Perpendiculars
161
Expression for Angle between two Tangents to a Conic see also p 189
163
Locus of intersection of Normals at extremities of a Focal Chord see also p 335 211
166
Chord subtending a right Angle at any point on Conic passes through a fixed
169
Supplemental Chords
171
Confocal Conics cut at Right Angles
181
how found
190
Expression for Parameter of Parabola given by general Equation
197
Radii Vectores through Foci have equal difference of Reciprocals
212
To inscribe in a Conic a Triangle whose sides pass through fixed Points see
273
Locus of intersection of Tangents which cut at right Angles see also pp 285 352 205
274
RECIPROCAL POLARS
276
Locus of Focus given four Tangents see also p 277
277
Polar of one Circle with regard to another
283
Relation between intercepts made by variable Tangent on two parallel Tangents
287
Carnots Theorem respecting Triangle cut by Conic see also p 319
290
Polar Equation of Parabola
292
Centre the Pole of the Line at infinity
296
Generalizations of Mac Laurins Method of generating Conics 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 Conics
306
System of Conics touching four Lines when cut a Transversal in Involution
313
Anharmonic Properties of Points and Tangents of a Conic see also pp 240 288
318
Projective proof of Carnots Theorem see also p 289
319
SECTIONS OF A CONE
326
Orthogonal Projection
332
Criterion whether Conics intersect in two real and two imaginary Points or not
337
Anharmonic ratio of four Points on a Conic abcd
342
Loci
343
Locus of free Vertex of a Polygon all whose sides touch one Conic and
350
Equation of reciprocal of two Conics having double contact
356
Area of common conjugate Triangle of two Conics
362
Three Conics 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
On systems of Tangential Coordinates
383
On systems of Conics satisfying four Conditions
389
Equation of Line at infinity
394
Focal Properties
396
Or on two Conjugate Diameters
399

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