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

Longmans, Green, Reader, and Dyer, 1869 - Conic sections - 377 pages

Distinction of Signs	3

Polar Coordinates	9

Discussion of Quadratic which determines Points where Line meets a Conic	22

Condition that three Lines may meet in a Point see also	23

Method of finding Coordinates of Foci of given Conie see also p 340	25

p	34

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

CHAPTER IV	53

Conjugate Hyperbola	211

Conics having double contact	215

Locus of Vertex of a Triangle inscribed in one Conic and whose sides touch	219

CHAPTER XIV	221

Director Circles of Conics touching four Lines have a common radical axis	233

Equation referred to two Tangents and their Chord	237

Polar of one Circle with regard to another	239

Expression for the Angles a Line makes with Axes	248

Angle between two Lines	60

Condition that six Points or Lines should form a system in Involution	62

RIGHT LINES	67

CHAPTER VI	75

Equation of Polar of a Point with regard to a Circle or Conic	84

Locus of intersection of Normals at extremities of a Focal Chord see also p 323 200	88

Condition that intercept by Circle on a given Line may subtend a right Angle	90

If a Point A lie on the polar of B B lies on the polar	98

its Properties	99

Diameters of parabola meet curve at infinity	103

Centres of Similitude	105

THE METHOD OF PROJECTION	106

To describe a Circle touching three given Circles see also pp 115 130 279	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

CHAPTER X	131

Conjugate Triangles Homologous	144

Transformation of general Equation to the centre	146

To draw a Normal through a given Point see also p 323	160

Geometrical construction for the Axes see also	168

Confocal Conics cut at right Angles	175

If two Chords meet in a Point Lines joining their extremities transversely meet	178

Intercepts on Chord between Curve and Asymptotes are equal	181

Figure of Hyperbola	188

Expression for Parameter of Parabola given by general Equation	189

Meaning of the Constants in Equation of a Right Line	198

228	204

53	205

232	210

Equation of a Conic having double contact with two given Conics	251

Meaning of the Equation SkS	252

Equation of pair of Tangents through a given Point see also p 144	257

To inscribe in a Conic a Triangle whose sides pass through fixed Points see	261

34 54	263

Locus of Centre of Conic touching four Lines	269

Reciprocation of Theorems concerning Angles at Focus	272

All Points at Infinity may be regarded as lying in a right Line	277

CHAPTER XVI	283

Generalizations of MacLaurins Method of generating Conics see also p 288	288

To inscribe in a Conic a Polygon whose sides pass through fixed Points	289

Proof that any Conic may be projected so as to become a Circle while a given	318

If a Chord of a Conic pass through a fixed Point O then tan PFO tan PFO	319

Condition that two Conics should touch	324

Equation of pair of Tangents whose Chord is a given Line	327

also p 333	333

General Equation of Director Circle	339

Four Conics having double contact with S and passing through three Points	345

INVOLUTION	346

THE METHOD OF INFINITESIMALS	350

Excess of sum of two Tangents over included Arc constant when Vertex moves	357

On systems of Tangential Coordinates	363

Property of Centre	368

Angle between two Lines	371

Locus of Pole of a given Line with regard to a Conic passing through four fixed	372

Distances of two Points from the centre proportional to the distance of each	373

Supplemental Chords	377

Given two conjugate diameters to find the axes

21

Title	A Treatise on Conic Sections: Containing an Account of Some of the Most Important Modern Algebraic and Geometric Methods A Treatise on Conic Sections: Containing an Account of Some of the Most Important Modern Algebraic and Geometric Methods, George Salmon
Author	George Salmon
Edition	5
Publisher	Longmans, Green, Reader, and Dyer, 1869
Original from	Harvard University
Digitized	16 Aug 2007
Length	377 pages

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