A Treatise on the Higher Plane Curves: Intended as a Sequel to a Treatise on Conic Sections

Hodges, Foster, 1873 - Conic sections - 379 pages

CHAPTER I	1

LINE COORDINATES	7

Number of terms in the general equation	13

Steiners and Kirkmans theorems on the hexagon	17

Their relation illustrated	24

Consideration of the case where the axis is a multiple tangent	30

Examples	36

Newtons process for determining form of curve at a singular point	44

Notation for general equation	182

Discriminant expressed in terms of fundamental invariants	189

The skew covariant	195

Equation expressed in four line coordinates	202

Illustration of the different forms	208

THE BITANGENTS	214

Scheme of these conics	221

bitangents the rest can be found by linear constructions	227

Multiple points and cusps how related to polar curves	50

Hessian and Steinerian defined	56

What singularities to be counted ordinary	62

Two forms in which problem of envelopes presents itself	65

Envelope of curve whose equation contains independent parameters	71

Its order in the coefficients of each curve	77

General expression for radius of curvature	83

Quasievolute when the absolute is a conic	89

CAUSTICS	95

Problem of negative pedals	102

METRICAL PROPERTIES	105

Curvilinear diameters	111

Sylvesters theory of residuation	113

Number of foci possessed by a curve	118

Locus of common vertex of two triangles whose bases are given and vertical	119

Locus of double focus of circular curve determined by N3 points	124

Maclaurins theory of correspondence of points on a cubic	130

Sixteen foci of a circular cubic lie on four circles	142

How related to triangle formed by tangents where line meets cubic	152

Plückers classification of cubics	158

Inscription of polygons in unicursal cubics	178

Generalization of the theory 353	179

Title	A Treatise on the Higher Plane Curves: Intended as a Sequel to a Treatise on Conic Sections
Author	George Salmon
Edition	2
Publisher	Hodges, Foster, 1873
Original from	Harvard University
Digitized	16 Aug 2007
Length	379 pages

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Foci of bicircular quartic lie on four circles	233

Caseys generation of bicircular quartics	234

Cartesians	241

Tangents at or from nodes touch the same conic	247

Covariant quartics	257

CHAPTER VII	263

Their evolutes are similar curves	269

310	270

Catenary	275

316	276

Cissoid its properties	281

CHAPTER VIII	282

Rational transformation between two curves	312

Theorem of constant deficiency derived from theory of elimination	319

CHAPTER IX	328

Bitangential of a quartic	336

Application to quartic	344

Steinerian of a curve	350

OSCULATING CONICS	356

Characteristics of systems of conics	362

Cayleys table of results	368

Acnodal cubic has real inflexions crunodal imaginary	375