An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
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Page viii
... Pole of a given Straight Line . Condition of Tangency . Condition for a Parabola Co - ordinates of the Centre ib . 54 ib . ib . 55 EXAMPLES 56 CHAPTER III . ELIMINATION BETWEEN LINEAR EQUATIONS . ARTS . viii CONTENTS .
... Pole of a given Straight Line . Condition of Tangency . Condition for a Parabola Co - ordinates of the Centre ib . 54 ib . ib . 55 EXAMPLES 56 CHAPTER III . ELIMINATION BETWEEN LINEAR EQUATIONS . ARTS . viii CONTENTS .
Page ix
... Pole of a given Straight Line སསཾ བྱཌསྤྱཙ 72 73 74 76 ib . 77 10 . Equation of the pair of Tangents , drawn to the Conic from a given external Point 78 II . Co - ordinates of the Centre 80 [ 2 . Equation of the Asymptotes 81 13 ...
... Pole of a given Straight Line སསཾ བྱཌསྤྱཙ 72 73 74 76 ib . 77 10 . Equation of the pair of Tangents , drawn to the Conic from a given external Point 78 II . Co - ordinates of the Centre 80 [ 2 . Equation of the Asymptotes 81 13 ...
Page x
... poles 106 109 18 . 19 . Polar reciprocal of one Circle with regard to another Reciprocation with respect to a Point IIO 112 20 . Instances of Transformation of Theorems by Reciprocation with respect to a circle ib . 21 . Corresponding ...
... poles 106 109 18 . 19 . Polar reciprocal of one Circle with regard to another Reciprocation with respect to a Point IIO 112 20 . Instances of Transformation of Theorems by Reciprocation with respect to a circle ib . 21 . Corresponding ...
Page xi
... Pole of a given straight line , and of the centre . Condition for a Parabola 127 9 . Circular points at infinity ib ... Poles , and Polars 13 . 138 139 14 . Any two conics may be projected into concentric curves 140 ARTS . PAGE 15 . Also ...
... Pole of a given straight line , and of the centre . Condition for a Parabola 127 9 . Circular points at infinity ib ... Poles , and Polars 13 . 138 139 14 . Any two conics may be projected into concentric curves 140 ARTS . PAGE 15 . Also ...
Page 46
... pole of CA with respect to the conic . Similarly , C , AB , stand to one another in the relation of pole and polar . Again , since the pole of AB is the point C , and the pole of AC is the point B , it follows that the line joining Band ...
... pole of CA with respect to the conic . Similarly , C , AB , stand to one another in the relation of pole and polar . Again , since the pole of AB is the point C , and the pole of AC is the point B , it follows that the line joining Band ...
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Common terms and phrases
a₁ aa+bB+cy Algebra angular points anharmonic ratio Arithmetic asymptotes auxiliary conic b₁ c₁ CAMBRIDGE CLASS BOOKS centre Chap chord cloth co-ordinates coefficients College common tangents condition conic passing conic section conics intersect Crown 8vo curve determine directrix ellipse find the equation fixed point focus four points given conic given point given straight line Hence hyperbola imaginary investigated line at infinity line joining locus meets the conic obtain pair parabola Pascal's Theorem perpendicular point f point of intersection points at infinity points of contact PQRS projection prove reciprocal polars represented respect right angles second degree Second Edition Similarly sin POS system of conics tangents tangents drawn theorem three points three straight lines touches the line Treatise triangle of reference U'bc ua² V'ca Vb² vß² W'ab wy² λα