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
... Pole of the Line at infinity ( see also p . 284 ) 149 150 150 Asymptotes of Curve 150 · · Equation of the Axes , how found 151 Functions of the Coefficients which are unaltered by transformation 152 Sum of Squares of Reciprocals of Semi ...
... Pole of the Line at infinity ( see also p . 284 ) 149 150 150 Asymptotes of Curve 150 · · Equation of the Axes , how found 151 Functions of the Coefficients which are unaltered by transformation 152 Sum of Squares of Reciprocals of Semi ...
Страница viii
... Pole ( see also pp . 244 , 272 ) 177 Line joining Focus to Pole of a Focal Chord is perpendicular to that Chord Polar Equation , Focus being Pole ( see p . 309 ) . 177 · 178 Segments of Focal Chord have constant Harmonic Mean 179 ...
... Pole ( see also pp . 244 , 272 ) 177 Line joining Focus to Pole of a Focal Chord is perpendicular to that Chord Polar Equation , Focus being Pole ( see p . 309 ) . 177 · 178 Segments of Focal Chord have constant Harmonic Mean 179 ...
Страница x
... Pole of a given Line with regard to a Conic passing through four fixed points ( see also pp . 148 , 256 , 260 , 290 ) 243 • or touching four right Lines ( see also pp . 256 , 265 , 269 , 309 , 327 ) 243 Focal properties of Conics 244 ...
... Pole of a given Line with regard to a Conic passing through four fixed points ( see also pp . 148 , 256 , 260 , 290 ) 243 • or touching four right Lines ( see also pp . 256 , 265 , 269 , 309 , 327 ) 243 Focal properties of Conics 244 ...
Страница xi
... Pole of a given Line 255 255 Condition that two Lines should be conjugate 256 Condition that a Line should tonch a Conic ( see also pp . 147 , 328 ) 255 Hearn's Method of finding Locus of Centre of a Conic , four conditions being given ...
... Pole of a given Line 255 255 Condition that two Lines should be conjugate 256 Condition that a Line should tonch a Conic ( see also pp . 147 , 328 ) 255 Hearn's Method of finding Locus of Centre of a Conic , four conditions being given ...
Страница xii
... Pole of the Line at infinity 284 · Asymptotes together with two Conjugate Diameters form Harmonic Pencil Lines from two fixed Points to a variable Point , how cut any Parallel to Asymptote 284 285 • · Parallels to Asymptotes through any ...
... Pole of the Line at infinity 284 · Asymptotes together with two Conjugate Diameters form Harmonic Pencil Lines from two fixed Points to a variable Point , how cut any Parallel to Asymptote 284 285 • · Parallels to Asymptotes through any ...
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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