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 vii
... Hyperbola 158 Conjugate Hyperbola 159 Asymptotes defined 150 , 159 Eccentricity of a Conic given by general Equation 159 Equations of Tangents and Polars 160 , 161 Expression for Angle between two Tangents to a Conic 161 Locus of ...
... Hyperbola 158 Conjugate Hyperbola 159 Asymptotes defined 150 , 159 Eccentricity of a Conic given by general Equation 159 Equations of Tangents and Polars 160 , 161 Expression for Angle between two Tangents to a Conic 161 Locus of ...
Страница viii
... Hyperbola , and 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 ...
... Hyperbola , and 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 ...
Страница ix
... Hyperbola , a fourth is given ( see also pp . 278 , 329 ) • • Circle circumscribing any self - conjugate Triangle with respect to an Equilateral Hyperbola passes through centre ( see also p . 310 ) Locus of intersection of Tangents ...
... Hyperbola , a fourth is given ( see also pp . 278 , 329 ) • • Circle circumscribing any self - conjugate Triangle with respect to an Equilateral Hyperbola passes through centre ( see also p . 310 ) Locus of intersection of Tangents ...
Страница xii
... Hyperbolas having same Focus and Directrix Reciprocals of equal Circles have same Parameter 273 274 Relation between ... Hyperbola Axes of Reciprocal , how found Reciprocal of Properties of Confocal Conics To describe a Circle touching ...
... Hyperbolas having same Focus and Directrix Reciprocals of equal Circles have same Parameter 273 274 Relation between ... Hyperbola Axes of Reciprocal , how found Reciprocal of Properties of Confocal Conics To describe a Circle touching ...
Страница xiii
... 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 Projection ...
... 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 Projection ...
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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