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
... 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 . Two Equations represent Points . A single Equation represents a Locus [ Geometric ...
... 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 . Two Equations represent Points . A single Equation represents a Locus [ Geometric ...
Страница iv
... given Right Lines Area of Triangle in terms of Co - ordinates of its Vertices Area of any Polygon • Condition that three Lines may meet in a Point ( see also Area of Triangle formed by three given Lines Equation of Line through the ...
... given Right Lines Area of Triangle in terms of Co - ordinates of its Vertices Area of any Polygon • Condition that three Lines may meet in a Point ( see also Area of Triangle formed by three given Lines Equation of Line through the ...
Страница v
... given by a single Equation Equation of Bisectors of Angles between these Lines PAGE 67 68 69 70 71 • 222 72 74 74 ... given Line meets a given Circle Imaginary Points General definition of Tangents 75 76 77 77 77 77 78 Condition that ...
... given by a single Equation Equation of Bisectors of Angles between these Lines PAGE 67 68 69 70 71 • 222 72 74 74 ... given Line meets a given Circle Imaginary Points General definition of Tangents 75 76 77 77 77 77 78 Condition that ...
Страница vi
... given Circles at equal Angles 108 · To describe a Circle touching three given Circles ( see also pp . 115 , 130 , 279 ) Mr. Casey's Solution of this Problem . 110 113 Relation connecting common Tangents of four Circles touched by same ...
... given Circles at equal Angles 108 · To describe a Circle touching three given Circles ( see also pp . 115 , 130 , 279 ) Mr. Casey's Solution of this Problem . 110 113 Relation connecting common Tangents of four Circles touched by same ...
Страница vii
... given ratio to those of concentric Circle 157 Figure 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 ...
... given ratio to those of concentric Circle 157 Figure 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 ...
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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