A Treatise on Conic Sections: Containing an Account of Some of the Most Important Modern Algebraic and Geometric MethodsLongmans, Green, and Company, 1879 - 399 páginas |
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Página iv
... , lie in a Right Line Equation of Line at infinity • Cartesian Equations a case of Trilinear Tangential Coordinates RRX 63 64 65 65 Reciprocal Theorems 66 CHAPTER V. RIGHT LINES . Meaning of an Equation resolvable iv CONTENTS .
... , lie in a Right Line Equation of Line at infinity • Cartesian Equations a case of Trilinear Tangential Coordinates RRX 63 64 65 65 Reciprocal Theorems 66 CHAPTER V. RIGHT LINES . Meaning of an Equation resolvable iv CONTENTS .
Página xi
... of Perpendiculars of circum- 275 scribing Triangle ( see also pp . 212 , 247 , 290 , 342 ) Locus of Focus given four Tangents ( see also p . 277 ) 275 27.5 CHAPTER XV . RECIPROCAL POLARS . PAGE Principle of Duality CONTENTS . xi.
... of Perpendiculars of circum- 275 scribing Triangle ( see also pp . 212 , 247 , 290 , 342 ) Locus of Focus given four Tangents ( see also p . 277 ) 275 27.5 CHAPTER XV . RECIPROCAL POLARS . PAGE Principle of Duality CONTENTS . xi.
Página xii
... Reciprocal in general 279 · Pascal's Theorem and Brianchon's mutually reciprocal 280 Radical Axes and Centres of Similitude of Conics having double contact with a given one 282 Polar of one Circle with regard to another 283 ...
... Reciprocal in general 279 · Pascal's Theorem and Brianchon's mutually reciprocal 280 Radical Axes and Centres of Similitude of Conics having double contact with a given one 282 Polar of one Circle with regard to another 283 ...
Página xiv
... reciprocal of two Conics having double contact Condition that they should touch each other 356 356 To draw a Conic having double contact with a given one , and touching three other such Conics 356 • Four Conics having double contact ...
... reciprocal of two Conics having double contact Condition that they should touch each other 356 356 To draw a Conic having double contact with a given one , and touching three other such Conics 356 • Four Conics having double contact ...
Página 66
... reciprocal theorems . - - Ex . Interpret in tangential coordinates the equations used in Art . 60 , Ex . 2 . Let a , ẞ , y denote the points A , B , C ' ; mß – ny , ny - la , la - mß , the points L , M , N ; then mß + ny − la , ny + la ...
... reciprocal theorems . - - Ex . Interpret in tangential coordinates the equations used in Art . 60 , Ex . 2 . Let a , ẞ , y denote the points A , B , C ' ; mß – ny , ny - la , la - mß , the points L , M , N ; then mß + ny − la , ny + la ...
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Outras edições - Ver tudo
A Treatise on Conic Sections: Containing an Account of Some of the Most ... George Salmon Visualização integral - 1879 |
A Treatise on Conic Sections: Containing an Account of Some of the Most ... George Salmon Pré-visualização indisponível - 2015 |
A Treatise on Conic Sections: Containing an Account of Some of the Most ... George Salmon Pré-visualização indisponível - 2016 |
Palavras e frases frequentes
anharmonic ratio asymptotes ax² axes bisected bisectors by² centre chord of contact circumscribing coefficients common tangents condition conic having double conic section conjugate diameters corresponding cos² denote determine directrix double contact drawn ellipse equal find the equation find the locus fixed line fixed point foci focus four points geometrically given conic given line given point Hence hyperbola imaginary points infinite distance inscribed intercept last Article 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 reciprocal rectangle right angles right line second degree sides sin² square substituting tangential equation theorem values vanish vertex vertices
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