An Elementary Treatise on Conic SectionsMacmillan, 1883 - 352 sider |
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Side viii
... foci of a conic 204 Eccentricities of a conic 205 Equations giving the foci 207 Equation of the axes 209 Equation of a conic referred to tangent and normal 211 Normals 211 Similar conics 215 Examples on Chapter X 219 CHAPTER XI ...
... foci of a conic 204 Eccentricities of a conic 205 Equations giving the foci 207 Equation of the axes 209 Equation of a conic referred to tangent and normal 211 Normals 211 Similar conics 215 Examples on Chapter X 219 CHAPTER XI ...
Side ix
... Foci of envelope • Meaning of the tangential equation S - XS ' = 0 Director - circles of conics which touch four given straight lines have a common radical axis . [ See also 308 and 319. ] Examples CHAPTER XIII . PAGE 238 240 241 244 ...
... Foci of envelope • Meaning of the tangential equation S - XS ' = 0 Director - circles of conics which touch four given straight lines have a common radical axis . [ See also 308 and 319. ] Examples CHAPTER XIII . PAGE 238 240 241 244 ...
Side x
Charles Smith. Condition for ellipse , parabola , or hyperbola Foci Equation of a circumscribing conic Equation of an inscribed conic PAGE 292 293 293 294 Equation of the inscribed circle 294 Conics through four fixed points 295 Conics ...
Charles Smith. Condition for ellipse , parabola , or hyperbola Foci Equation of a circumscribing conic Equation of an inscribed conic PAGE 292 293 293 294 Equation of the inscribed circle 294 Conics through four fixed points 295 Conics ...
Side 58
... foci . -- It is clear that when the two foci are given the involu- tion is completely determined . An involution is also completely determined when two pairs of conjugate points are given . For , let a , a and b , b ' be the distances ...
... foci . -- It is clear that when the two foci are given the involu- tion is completely determined . An involution is also completely determined when two pairs of conjugate points are given . For , let a , a and b , b ' be the distances ...
Side 59
... foci form a harmonic range . Let K , K , be the two foci , and O the centre of the involution , and let K , O = c = OK2 . Then , if P , P ' be the two conjugates we have to prove that 2 K‚P.K , P ' K1P.K‚P == or ( c + OP ) ( OP ' — c ) ...
... foci form a harmonic range . Let K , K , be the two foci , and O the centre of the involution , and let K , O = c = OK2 . Then , if P , P ' be the two conjugates we have to prove that 2 K‚P.K , P ' K1P.K‚P == or ( c + OP ) ( OP ' — c ) ...
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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 circumscribing coefficients College confocal conics conjugate diameters conjugate hyperbola constant corresponding cross ratio Crown 8vo curve diagonals directrix distance eccentric angles Edition ellipse envelope equal angles Extra fcap fcap find the equation find the locus fixed point fixed straight line foci focus four points given points given straight line harmonic Hence imaginary inscribed latus rectum Let the co-ordinates Let the equation line joining line whose equation meet middle point nine-point circle normals pair of conjugate parabola pass pencil perpendicular point of intersection point Q points at infinity points of contact polar pole Professor projection prove quadrilateral radical axis rectangular hyperbola required equation right angles shew sides square subtend tangents triangle of reference values vertex zero
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