An Elementary Treatise on Conic SectionsMacmillan and Company, 1894 - 352 sider |
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Resultat 1-5 av 7
Side x
... circle 294 Conics through four fixed points 295 Conics touching four fixed lines 296 Conics with respect to which ... nine - point circle 299 Pascal's theorem . [ See also 328. ] 299 Brianchon's theorem 301 • AREAL CO - ORDINATES 302 ...
... circle 294 Conics through four fixed points 295 Conics touching four fixed lines 296 Conics with respect to which ... nine - point circle 299 Pascal's theorem . [ See also 328. ] 299 Brianchon's theorem 301 • AREAL CO - ORDINATES 302 ...
Side 236
... circle , the centre - locus is a rectangular hyperbola . If aa ' – bb ' , and the axes are at right angles , all the ... nine- point circle . 211. The asymptotes of any conic through the four points defined as in Art . 206 , are parallel ...
... circle , the centre - locus is a rectangular hyperbola . If aa ' – bb ' , and the axes are at right angles , all the ... nine- point circle . 211. The asymptotes of any conic through the four points defined as in Art . 206 , are parallel ...
Side 298
... , a + μc + vb = 0 , b + va + λc = 0 , and c + λb + μa = 0 . Whence λ = — cos А , μ = = 298 NINE - POINT CIRCLE . Conics referred to two tangents and the chord of contact The circle with respect to which the triangle of reference self-polar.
... , a + μc + vb = 0 , b + va + λc = 0 , and c + λb + μa = 0 . Whence λ = — cos А , μ = = 298 NINE - POINT CIRCLE . Conics referred to two tangents and the chord of contact The circle with respect to which the triangle of reference self-polar.
Side 299
... nine - point circle . Let the equation of the circle be - aßy + bya + caẞ − ( λa + μß + vy ) ( aa + bB + cy ) = 1 ) . This circle cuts a = 0 where bß = cy ; .. abc - 2 ( μc + vb ) bc = 0 , μ ע a2 + = 2abc Similarly and Hence ע + 210 ...
... nine - point circle . Let the equation of the circle be - aßy + bya + caẞ − ( λa + μß + vy ) ( aa + bB + cy ) = 1 ) . This circle cuts a = 0 where bß = cy ; .. abc - 2 ( μc + vb ) bc = 0 , μ ע a2 + = 2abc Similarly and Hence ע + 210 ...
Side 311
... circle . Shew that its major and minor axes are R + d and R - d respectively , R being the radius of the ... nine - point circle . 19. Shew that the locus of the foci of all conics touching the four lines la ± mß ± ny = 0 is the cubic Pi ...
... circle . Shew that its major and minor axes are R + d and R - d respectively , R being the radius of the ... nine - point circle . 19. Shew that the locus of the foci of all conics touching the four lines la ± mß ± ny = 0 is the cubic Pi ...
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An Elementary Treatise on Conic Sections by the Methods of Co-ordinate Geometry Charles Smith Uten tilgangsbegrensning - 1921 |
Vanlige uttrykk og setninger
2hxy a² b2 angular points asymptotes ax² axes bisect by² Cambridge centre coincident common confocal conics conic touching conjugate diameters constant corresponding Crown 8vo curve diagonals director-circle directrix distance eccentric angles Edition ellipse equal angles Extra fcap fcap find the equation find the locus fixed point fixed straight line foci focus four given points four points given conic given straight line imaginary inscribed latus rectum Let the equation line at infinity line joining line whose equation locus meet middle point nine-point circle normals original conic parabola Pascal's Theorem perpendicular point of intersection points at infinity points of contact polar pole Professor prove quadrilateral radical axis radius ratio rectangular hyperbola right angles second degree self-polar shew sides square tangential equation tangents triangle formed triangle of reference Trinity College values vertex vß² x² y² zero
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