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 - 399 pàgines
 

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Equation of Asymptotes of a Conic given by general Equation see also p 340
272
To inscribe in a Conic a Triangle whose sides pass through fixed Points see
273
RECIPROCAL POLARS
276
Polar of one Circle with regard to another
283
Two Equations represent Points
290
Centre the Pole of the Line at infinity
296
Generalizations of Mac Laurins Method of generating Conics see also p 300 251
300
Criterion whether two Systems of Points be Homographic see also p 383
304
INVOLUTION
307
System of Conics touching four Lines when cut a Transversal in Involution
313
Anharmonic Properties of Points and Tangents of a Conic see also pp 240 288
318
Projective proof of Carnots Theorem see also p 289
319
SECTIONS OF A CONE
326
Orthogonal Projection
332
Criterion whether Conics intersect in two real and two imaginary Points or not
337
Anharmonic ratio of four Points on a Conic abcd atcd if the Lines
342
Tangential equation of four Points common to two Conics
343
Meaning of the Constants in Equation of a Right Line
349
Envelope of Base of Triangle inscribed in one Conic two of whose sides touch
350
Equation of reciprocal of two Conics having double contact
356
Area of common conjugate Triangle of two Conics
360
CHAPTER XIX
369
Excess of sum of two Tangents over included Arc constant when Vertex moves
377
Theorems on complete Figure formed by six Points on a Conic
383
On systems of Conics satisfying four Conditions
389
GENERAL EQUATION OF SECOND DEGREE
394
Envelope of Chord joining corresponding Points of two homographic systems
396

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