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 páginas |
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Página vii
... Ellipse , centre being Pole 155 Figure of Ellipse investigated 156 Geometrical construction for the Axes ( see also p . 168 ) 156 Ordinates of Ellipse in given ratio to those of concentric Circle 157 Figure of Hyperbola 158 Conjugate ...
... Ellipse , centre being Pole 155 Figure of Ellipse investigated 156 Geometrical construction for the Axes ( see also p . 168 ) 156 Ordinates of Ellipse in given ratio to those of concentric Circle 157 Figure of Hyperbola 158 Conjugate ...
Página viii
... Ellipse ( see also p . 316 ) 180 ASYMPTOTES : how found 180 Intercepts on Chord between Curve and Asymptotes are equal 181 Lines joining two fixed to variable Point make constant Intercept on Asymptote Constant area cut off by tangent ...
... Ellipse ( see also p . 316 ) 180 ASYMPTOTES : how found 180 Intercepts on Chord between Curve and Asymptotes are equal 181 Lines joining two fixed to variable Point make constant Intercept on Asymptote Constant area cut off by tangent ...
Página ix
... ellipse from any point Radii Vectores through Foci have equal difference of Reciprocals Examples on Parabola Three Perpendiculars of Triangle formed by three Tangents intersect on 201 • 201 201 Directrix ( see also pp . 236 , 263 , 278 ...
... ellipse from any point Radii Vectores through Foci have equal difference of Reciprocals Examples on Parabola Three Perpendiculars of Triangle formed by three Tangents intersect on 201 • 201 201 Directrix ( see also pp . 236 , 263 , 278 ...
Página xii
... Ellipse , Hyperbola or Parabola ; when Equilateral Hyperbola Axes of Reciprocal , how found Reciprocal of Properties of Confocal Conics To describe a Circle touching three given Circles How to form Equation of Reciprocal 277 • 278 279 ...
... Ellipse , Hyperbola or Parabola ; when Equilateral Hyperbola Axes of Reciprocal , how found Reciprocal of Properties of Confocal Conics To describe a Circle touching three given Circles How to form Equation of Reciprocal 277 • 278 279 ...
Página xiii
... Ellipse , Hyperbola , or Parabola Every Parabola has a Tangent at an infinite Distance 314 315 · > 316 317 · Proof that any Conic may be projected so as to become a Circle , while a given Line passes to Infinity 318 Orthogonal ...
... Ellipse , Hyperbola , or Parabola Every Parabola has a Tangent at an infinite Distance 314 315 · > 316 317 · Proof that any Conic may be projected so as to become a Circle , while a given Line passes to Infinity 318 Orthogonal ...
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Términos y frases comunes
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