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

Longman, Brown, Green, and Longmans, 1855 - 324 Seiten

CHAPTER I	1

Distance between two Points	10

Investigation of Loci	30

Loci solved by Polar Coordinates	46

of a Homogeneous Equation of the nth Degree	62

THE CIRCLE	70

Equation of Tangent to a Circle at a given Point	78

Condition that four Points should lie on a Circle and its Geometrical meaning	84

CHAPTER XII	175

Intercept on Axis by two Lines equal to projection of distance between their Poles	181

CHAPTER XIII	188

Given three Points on Equilateral Hyperbola a fourth is given	195

SIMILAR CONIC SECTIONS	201

Anharmonic Property of Conics proved see also p 225	203

Meaning of the Constants in Equation of a Right Line	210

Diagonals of inscribed and circumscribed Quadrilateral pass through the same Point	218

If two Chords meet in a Point Lines joining their extremities transversely meet	90

CHAPTER VIII	97

PROPERTIES OF TWO OR MORE CIRCLES	103

Geometrical meaning of the Equation	104

Ordinates of Ellipse in given ratio to those of concentric Circle	111

Coordinates of Point cutting that Distance in a given Ratio	119

Coordinates of centre of Conic	126

Harmonic Property of Polars see also p 272	132

152	135

CHAPTER XI	138

Supplemental Chords	156

Sum or difference of Focal Radii constant	162

Polar Equation of Parabola	167

Angle subtended at the Focus by a Chord bisected by Line joining Focus to its Pole	168

Expression for the Angles a Line makes with Axes	231

Length of Perpendicular from a Point on a Line	238

Condition that Equation of second Degree should represent Right Lines see also	250

CHAPTER XV	253

Asymptotes together with two Conjugate Diameters form Harmonic Pencil	273

To inscribe a Polygon in a Conic whose sides pass through fixed Points	280

Proof of Pascals Theorem	283

METHOD OF INFINITESIMALS	289

Area of Triangle in terms of Coordinates of its Vertices	290

Determination of Radii of Curvature	295

Equation of Polar of a Point with regard to a Conic given by the general	310

NOTES	317

Coordinates of Intersection of two Right Lines	1

Titel	A Treatise on Conic Sections: Containing an Account of Some of the Most Important Modern Algebraic and Geometric Methods
Autor/in	George Salmon
Ausgabe	3
Verlag	Longman, Brown, Green, and Longmans, 1855
Original von	Universität La Sapienza Rom (Biblioteca di Matematica G. Castelnuovo)
Digitalisiert	3. Mai 2013
Länge	324 Seiten

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