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 - Conic sections - 399 pages
 

Contents

Equation of pair of Tangents through a given Point see also p 149
269
Loci
271
RECIPROCAL POLARS
276
Carnots Theorem respecting Triangle cut by Conic see also p 319
289
EXAMPLES ON CONICS
295
To inscribe in a Conic a Polygon whose sides pass through fixed Points
301
Analytic condition that four Points should form a Harmonic System
305
System of Conics through four Points cut any Transversal in Involution
311
Projective Properties of a Quadrilateral 817
319
SECTIONS OF A CONE
326
Orthogonal Projection
332
Criterion whether Conics intersect in two real and two imaginary Points or not
337
Tangential equation of four Points common to two Conics
343
Envelope of Base of Triangle inscribed in one Conic two of whose sides touch
350
Middle Points of Diagonals of a Quadrilateral are in a Right Line see also p
376
Excess of sum of two Tangents over included Arc constant when Vertex moves
377
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
Proof that middle Points of Diagonals of Quadrilateral lie in a Right Line
384
On systems of Conics satisfying four Conditions
389
Circles circumscribing the Triangles formed by four Lines meet in a Point
391
164
393
Equation of Line at infinity
394
Distances of two Points from the centre proportional to the distance of each
395
Focal Properties
396
Generalizations of Mac Laurins Method of generating Conics see also p 300
398
Supplemental Chords
399

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