A Treatise on Conic Sections: Containing an Account of Some of the Most Important Modern Algebraic and Geometric MethodsLongmans, Green, Reader, and Dyer, 1869 - 377 страници |
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Страница iv
... of Bisectors of Sides , and of Perpendiculars at Equation of Line at infinity · Cartesian Equations a case of Trilinear Tangential Co - ordinates Reciprocal Theorems CHAPTER V. RIGHT LINES . Meaning of an Equation resolvable iv CONTENTS .
... of Bisectors of Sides , and of Perpendiculars at Equation of Line at infinity · Cartesian Equations a case of Trilinear Tangential Co - ordinates Reciprocal Theorems CHAPTER V. RIGHT LINES . Meaning of an Equation resolvable iv CONTENTS .
Страница xi
... ) 263 CHAPTER XV . RECIPROCAL POLARS . Principle of Duality Locus of Centre of Conic touching four Lines Locus of Focus of Conic touching four Lines 264 265 265 PAGE Director Circles of Conics touching four Lines have a CONTENTS . xi.
... ) 263 CHAPTER XV . RECIPROCAL POLARS . Principle of Duality Locus of Centre of Conic touching four Lines Locus of Focus of Conic touching four Lines 264 265 265 PAGE Director Circles of Conics touching four Lines have a CONTENTS . xi.
Страница xii
... Reciprocal in general Pascal's Theorem and Brianchon's mutually reciprocal 265 267 • 268 • · Polar of one Circle with regard to another Radical Axes and Centres of Similitude of Conics having double contact with a given one 270 · 271 ...
... Reciprocal in general Pascal's Theorem and Brianchon's mutually reciprocal 265 267 • 268 • · Polar of one Circle with regard to another Radical Axes and Centres of Similitude of Conics having double contact with a given one 270 · 271 ...
Страница xiv
... reciprocal of two Conics having double contact Condition that they should touch each other 342 • 343 To draw a Conic having double contact with a given one , and touching three other such Conics 343 Four Conics having double contact ...
... reciprocal of two Conics having double contact Condition that they should touch each other 342 • 343 To draw a Conic having double contact with a given one , and touching three other such Conics 343 Four Conics having double contact ...
Страница xv
... = 02123 −4 ( 1220133 + 211233 +03110322 ) + 12§ ; where is the invariant , corresponding to 123 , formed with the coefficients of the reciprocal systems . " ANALYTIC GEOMETRY . CHAPTER I. THE POINT . 1. THE CONTENTS . XV.
... = 02123 −4 ( 1220133 + 211233 +03110322 ) + 12§ ; where is the invariant , corresponding to 123 , formed with the coefficients of the reciprocal systems . " ANALYTIC GEOMETRY . CHAPTER I. THE POINT . 1. THE CONTENTS . XV.
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anharmonic ratio asymptotes ax² axes bisected bisectors chord of contact circumscribing coefficients common tangents condition conic section conjugate diameters corresponding cos² denote determine directrix double contact drawn ellipse equal find the co-ordinates find the equation find the locus fixed lines fixed point foci focus four points given circles given line given point Hence hyperbola imaginary points infinite distance inscribed intercept joining the points last Article length line at infinity line joining line meets meet the curve middle points origin parabola parallel Pascal's theorem perpendicular point of contact point x'y points at infinity points of intersection polar polar equation pole proved quadratic quadrilateral radical axis radius vector rectangle right angles right line second degree sides sin² square substituting tangential equation theorem values vanish vertex vertices