An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory Projections |
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Page vi
... where the demonstrations were imperfect or obscure , and have added some examples , taken from various Cambridge Examination papers . DECEMBER , 1875 . CONTENTS . CHAPTER I. TRILINEAR CO - ORDINATES . EQUATION vi PREFACE .
... where the demonstrations were imperfect or obscure , and have added some examples , taken from various Cambridge Examination papers . DECEMBER , 1875 . CONTENTS . CHAPTER I. TRILINEAR CO - ORDINATES . EQUATION vi PREFACE .
Page vii
... EXAMPLES 21 • • 19 . Definitions 20 . 21 . ANHARMONIC RATIO . The Anharmonic Ratio of a Pencil is equal to that of the range in which it is cut by any Transversal Definition of an Harmonic Pencil 23 • ib . • 225 25 ARTS . 22 . The ...
... EXAMPLES 21 • • 19 . Definitions 20 . 21 . ANHARMONIC RATIO . The Anharmonic Ratio of a Pencil is equal to that of the range in which it is cut by any Transversal Definition of an Harmonic Pencil 23 • ib . • 225 25 ARTS . 22 . The ...
Page viii
... . 27 . Pole of a given Straight Line Condition of Tangency . Condition for a Parabola Co - ordinates of the Centre . ib . ib . 55 • EXAMPLES . 56 CHAPTER III . ELIMINATION BETWEEN LINEAR EQUATIONS . ARTS . viii CONTENTS .
... . 27 . Pole of a given Straight Line Condition of Tangency . Condition for a Parabola Co - ordinates of the Centre . ib . ib . 55 • EXAMPLES . 56 CHAPTER III . ELIMINATION BETWEEN LINEAR EQUATIONS . ARTS . viii CONTENTS .
Page ix
... EXAMPLES 287 ib . 69 71 CHAPTER IV . ON THE CONIC REPRESENTED BY THE GENERAL EQUATION OF THE SECOND DEGREE . 2 . 3 . To find the point in which a straight line , drawn in a given direction through a given point of the conic , meets the ...
... EXAMPLES 287 ib . 69 71 CHAPTER IV . ON THE CONIC REPRESENTED BY THE GENERAL EQUATION OF THE SECOND DEGREE . 2 . 3 . To find the point in which a straight line , drawn in a given direction through a given point of the conic , meets the ...
Page x
... EXAMPLES . 388 96 98 CHAPTER V. TRIANGULAR CO - ORDINATES . 1. Definition of the Triangular Co - ordinates of a Point 100 2 . Formulæ relating to Straight Lines ib . 3 . Formulæ relating to Conics 102 CHAPTER VI . RECIPROCAL POLARS . 3 ...
... EXAMPLES . 388 96 98 CHAPTER V. TRIANGULAR CO - ORDINATES . 1. Definition of the Triangular Co - ordinates of a Point 100 2 . Formulæ relating to Straight Lines ib . 3 . Formulæ relating to Conics 102 CHAPTER VI . RECIPROCAL POLARS . 3 ...
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Common terms and phrases
aa+bB+cy angular points asymptotes auxiliary conic b₁ Brianchon's Theorem C₁ centre Chap chord co-ordinates coefficients common tangents conic passing conic section determinant directrix find the equation fixed point fixed straight line focus follows four points given conic given point given straight line Hence imaginary internal bisectors investigated Let the equation line at infinity locus meets the conic nine-point circle obtain opposite sides pair parabola Pascal's Theorem perpendicular point f point of intersection points at infinity points of contact polar reciprocal projection prove radical axis reciprocal curve reciprocated with respect rectangular hyperbola represented right angles second degree similar and similarly system of conics tangents drawn theorem three points three straight lines triangle of reference ua² uf+w'g+v'h Vb² vß² W'ab Wc² whence wy²