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

Longmans, Green, and Company, 1879 - 399 pages

CHAPTER XIX	1

Des Cartes Method of Coordinates	3

Discussion of Quadratic which determines Points where Line meets a Conic	8

Polar Coordinates	12

Condition that three Lines may meet in a Point see also p	34

Problems where it is proved that a Moveable Line always passes through	45

CHAPTER IV	53

Meaning of the Constants in Equation of a Right Line	57

10	231

CHAPTER XIV	232

Focal properties of Conics see also pp 267 277 281 321 339	236

Property of Chords of Intersection of two Conics each having double contact	242

11	274

RECIPROCAL POLARS	276

Polar of one Circle with regard to another	283

Carnots Theorem respecting Triangle cut by Conic see also p 319	289

RIGHT LINES	67

Circular Loci	88

pp 320 353	96

The limiting Points of the system	98

its Properties	99

Diameters of Parabola meet Curve at infinity	103

To draw a Normal through a given Point see also p 335	106

Quadrilateral	113

Quantities unchanged by Inversion	116

Length of Tangent to a Circle in Trilinear Coordinates	129

CHAPTER X	136

Locus of Point whence Tangents to two Conics form a Harmonic Pencil see	146

Condition that a given Line should touch a Conic see also pp 267 340	153

39	158

Polar Equation of Ellipse centre being Pole	160

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

Geometrical construction for the Axes see also p 173	173

Confocal Conics cut at Right Angles	181

If two Chords meet in a Point Lines joining their extremities transversely meet	184

how found	190

Figure of Hyperbola	199

47	208

Radii Vectores through Foci have equal difference of Reciprocals	209

Transformation of the Equation to the form y²	214

Meaning of Constant k in Equation a	216

Conjugate Hyperbola	222

Polar Equation of Parabola	292

CHAPTER XVI	295

Algebraic Expression for Anharmonic Ratio of a Pencil	299

To inscribe in a Conic a Polygon whose sides pass through fixed Points	301

Condition that Line should be cut Harmonically by two Conics	306

System of Conics touching four Lines when cut a Transversal in Involution	313

Projective proof of Carnots Theorem see also p 289	319

Expression of Equation of any Right Line in terms of three given ones	321

SECTIONS OF A CONE	326

Locus of Pole with respect to a series of Confocal Conics	331

Orthogonal Projection	332

Criterion whether Conics intersect in two real and two imaginary Points or not	337

19	346

Locus of Vertex of a Triangle inscribed in one Conic and whose sides touch	349

Envelope of Base of Triangle inscribed in one Conic two of whose sides touch	350

touching three Lines are touched by the same Conics	359

Tangent to any Conic cuts off constant Area from similar and concentric Conic	373

If three Conics have a common Chord their other Chords intersect in a Point	379

Envelope of Line joining corresponding Points of two Homographic Systems	383

On the Problem to describe a Conic under five conditions	386

of Line joining two Points	387

Angle between two Lines	393

GENERAL EQUATION OF SECOND DEGREE	394

Distances of two Points from the centre proportional to the distance of each	395

Equation of Circle cutting three Circles orthogonally	396

201	397

65	399

Title	A Treatise on Conic Sections: Containing an Account of Some of the Most Important Modern Algebraic and Geometric Methods
Author	George Salmon
Edition	6
Publisher	Longmans, Green, and Company, 1879
Original from	the University of Wisconsin - Madison
Digitized	22 Aug 2008
Length	399 pages

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