## Re: [EMHL] new conique

Expand Messages
• 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
• 0 Attachment
Dear Bernard and Nikolaos
Thanks you very much for your responses
It will be useful for me
Amically
Michel

wrote:
>
> Dear Michel
> 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
>
>
> > 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 uÂ²+mpvÂ²+mnwÂ²-(mÂ²+np)vw-(nÂ²+mp)wu-(pÂ²+mn)uv = 0
> > If F is the centroÃ¯d 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
> >
> >
> >
> >
> > ------------------------------------
> >
> >
> >
> >
>
>
> ___________________________________________________________
> Î§ÏÎ·ÏÎ¹Î¼Î¿ÏÎ¿Î¹ÎµÎ¯ÏÎµ Yahoo!;
> Î'Î±ÏÎµÎ¸Î®ÎºÎ±ÏÎµ ÏÎ± ÎµÎ½Î¿ÏÎ»Î·ÏÎ¹ÎºÎ¬ Î¼Î·Î½ÏÎ¼Î±ÏÎ±
(spam); Î¤Î¿ Yahoo! Mail
> Î´Î¹Î±Î¸Î­ÏÎµÎ¹ ÏÎ·Î½ ÎºÎ±Î»ÏÏÎµÏÎ· Î´ÏÎ½Î±ÏÎ®
ÏÏÎ¿ÏÏÎ±ÏÎ¯Î± ÎºÎ±ÏÎ¬ ÏÏÎ½ ÎµÎ½Î¿ÏÎ»Î·ÏÎ¹ÎºÏÎ½