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 v
... extremities transversely meet on its Polar 92 26 • 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 ...
... extremities transversely meet on its Polar 92 26 • 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 ...
Página viii
... a series of Confocal Conics 198 If a Chord of a Conic pass through a fixed Point O , then tan PFO.tan P'FO is constant ( see also p . 319 ) 199 PAGE Locus of intersection of Normals at extremities of a viii CONTENTS .
... a series of Confocal Conics 198 If a Chord of a Conic pass through a fixed Point O , then tan PFO.tan P'FO is constant ( see also p . 319 ) 199 PAGE Locus of intersection of Normals at extremities of a viii CONTENTS .
Página ix
... extremities of a Focal Chord ( see also p . 323 ) 200 Expression for angle between tangents to ellipse from any point Radii Vectores through Foci have equal difference of Reciprocals Examples on Parabola Three Perpendiculars of Triangle ...
... extremities of a Focal Chord ( see also p . 323 ) 200 Expression for angle between tangents to ellipse from any point Radii Vectores through Foci have equal difference of Reciprocals Examples on Parabola Three Perpendiculars of Triangle ...
Página xiii
... extremities of Chords passing through a given Point 323 Condition that two Conics should touch 324 Criterion whether Conies intersect in two real and two imaginary Points or not 325 Equation of Curve parallel to a Conic Equation of ...
... extremities of Chords passing through a given Point 323 Condition that two Conics should touch 324 Criterion whether Conies intersect in two real and two imaginary Points or not 325 Equation of Curve parallel to a Conic Equation of ...
Página 39
... extremity of the perpendicular . Take the same axes , and let us inquire what relation exists between the co - ordi- nates of the point whose locus we are seeking . The x of this point plainly is MR , and the y is , by hypothesis , AC ...
... extremity of the perpendicular . Take the same axes , and let us inquire what relation exists between the co - ordi- nates of the point whose locus we are seeking . The x of this point plainly is MR , and the y is , by hypothesis , AC ...
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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