8752Two Emile Hyacinthe Lemoine centers
- Dec 1, 2003Dear Hyacinthists
looking at the beginning of the very interesting from EH Lemoyne :
Suite de theoremes et de resultats concernant la geometrie du
I see that he discovered the following centers :
1) Ma is the unique point on the segment BC such as
MaB + d(Ma,AB) = MaC + d(Ma, AC) with d for distance; define Mb, Mc
cyclically. Then MaMbMc and ABC are perspective at the point of the
line IG with trilinear 1+2R/a:...
2) Na is the unique point on the segment BC such as
NaB + d(Na,AC) = NaC + d(Na, AB) with d for distance; define Nb, Nc
cyclically. Then NaNbNc and ABC are perspective at the point of the
line IG with trilinear (2R/a)-1:...
I don't think - but, may be, I'm wrong - that these points are in
the current ETC.
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