On Wed, 9 Aug 2000, Bernard Gibert wrote:
> > In my work, I've been using the following ad hoc nomenclature:
> > lines through P orthogonal to PA, PB, PC: orthocevians (of P)
> > intersections of orthocevians with opposite sides: orthocevian feet
> > (but I like Bernard Gibert's "orthotraces" better)
> > line connecting the orthotraces: orthocevian line or orthocevian
> > axis
> > tripole of orthocevian line: orthopoint
> I do not mind at all to change my denominations : they were temporary and
> maybe a bit clumsy because there is no polarity underneath.
> May I propose we stick to :
> orthocevians, orthotraces, orthocevian line, orthopoint or orthoconjugate
> [ I far prefer orthoconjugate], orthoassociate,, antiorthoconjugates...
I agree with all of these except "orthoconjugate" I'm afraid
(and correspondingly "antiorthoconjugate" of course). I think this is
very likely to mislead, because it's usually understood in mathematics
that "conjugacy" is used for a symmetrical 1-1 relation. Since your
"orthoconjugacy" is an asymmetric 2-1 relation, it's an inappropriate
On the other hand, "orthopoint" seems a bit weak, so I don't much
like that either! A better word would be "orthopole", if it weren't
for the fact that that's already been used for a different relation,
because after all it's the tripole of the orthocevian line. Perhaps
"orthoimage", though I can't work up much enthusiasm even for that.
"Orthocevian point" is wonderfully descriptive (as was "orthocevian
line"), but is a bit long. How about that as the full form, and
"orthoceviant" as a slangy abbreviation?