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Re: [EMHL] new conique

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  • michgarl
    Dear Bernard and Nikolaos Thanks you very much for your responses It will be useful for me Amically Michel ... (spam); Το Yahoo! Mail ... προστασία
    Message 1 of 5 , May 1, 2008
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      Dear Bernard and Nikolaos
      Thanks you very much for your responses
      It will be useful for me
      Amically
      Michel

      --- In Hyacinthos@yahoogroups.com, Nikolaos Dergiades <ndergiades@...>
      wrote:
      >
      > Dear Michel
      > I don't know to answer your question.
      > This conic also becomes a circle if M = X(194)
      > the anticomplement of the isotomic conjugate
      > of the Lemoine point X(6).
      > If have no error it becomes a parabola if M lies on the quartic
      > 3(x^4+y^4+z^4)-2(x^3+y^3+z^3-xyz)(x+y+z)-5(xy+yz+zx)^2=0
      > Best regards
      > Nikos Dergiades
      >
      >
      > > Dear Hyacinthos
      > > In triangle (ABC), point M= [m:n:p] has for cevian triangle
      > > (PQR),
      > > with P =[0:n:p], Q = [m:0:p], R=[m:n:0]
      > > Parallel line through P to (AC) cuts (AB) in Cp = [p:n:0]
      > > Parallel line through P to (AB) cuts (AC) in Bp = [n:0:p]
      > > So are Aq,Cq,Ar,Br
      > > Those six points lie on a same conic with barycentric
      > > equation
      > > np u²+mpv²+mnw²-(m²+np)vw-(n²+mp)wu-(p²+mn)uv = 0
      > > If F is the centroïd of (ABC), this conic is the inscrit
      > > conic of
      > > Steiner, with center G
      > > file "conique1" with figure is add to the forum
      > >
      > > Is that known in math litterature?
      > >
      > > Amically
      > >
      > > Michel
      > >
      > >
      > >
      > >
      > > ------------------------------------
      > >
      > > Yahoo! Groups Links
      > >
      > >
      > >
      >
      >
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