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 iii
... Distance between two Points Its sign Co - ordinates of Point cutting that Distance in a given Ratio Transformation of Co - ordinates does not change Degree of an Equation Polar Co - ordinates PAGE 2 8 5 10 CHAPTER II . THE RIGHT LINE ...
... Distance between two Points Its sign Co - ordinates of Point cutting that Distance in a given Ratio Transformation of Co - ordinates does not change Degree of an Equation Polar Co - ordinates PAGE 2 8 5 10 CHAPTER II . THE RIGHT LINE ...
Страница v
... Distances of two Points from the centre , proportional to the distance of each from Polar of other Expression of Co - ordinates of Point on Circle by auxiliary Angle Problems where a variable Line always touches a Circle Examples on ...
... Distances of two Points from the centre , proportional to the distance of each from Polar of other Expression of Co - ordinates of Point on Circle by auxiliary Angle Problems where a variable Line always touches a Circle Examples on ...
Страница vi
... Distance between two Points expressed in Trilinear Co - ordinates Determinant Notation • Determinant expressions for Equations of Circles through three Points , or cutting three at right Angles Relation connecting mutual distances of ...
... Distance between two Points expressed in Trilinear Co - ordinates Determinant Notation • Determinant expressions for Equations of Circles through three Points , or cutting three at right Angles Relation connecting mutual distances of ...
Страница viii
... distance between their Poles 189 190 · Subnormal Constant Locus of foot of Perpendicular from Focus on Tangent 191 193 • Locus of intersection of Tangents which cut at right Angles ( see also 273 , 339 ) Angle between two Tangents half ...
... distance between their Poles 189 190 · Subnormal Constant Locus of foot of Perpendicular from Focus on Tangent 191 193 • Locus of intersection of Tangents which cut at right Angles ( see also 273 , 339 ) Angle between two Tangents half ...
Страница xiii
... 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 Determination of Focus of Section of a right Cone Locus of Vertices of right ...
... 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 Determination of Focus of Section of a right Cone Locus of Vertices of right ...
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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