HYACINTHOS 2929

Dear John,

At 02:47 PM 5/29/01 -0400, you wrote:

>On Tue, 29 May 2001 yiu@fau.edu wrote:
>
>> u:v:w = q/b+r/c-p/a : r/c+p/a-q/b : p/a+q/b-r/c.
>>
>> In particular, if p:q:r=1:1:1, this is the equal-parallelian point.
>
> What's the origin of this name?

I found this in [TCCT], where Clark called the point X(182) ``equal
parallelians point''. It appeared in Vigarie's ``19th century of
Encyclopedia of triangle centers''.
Vigarie wrote:

``Ce point remarquable est le point anticompl\'ementaire du point
r\'eciproque du centre du cercle inscrit; nous l'appellerons plus
simplement {\em centre des parall\`eles \'egales}.''

He gave the following references:

E.~Hain. -- A.G.H. tome 57, p.400; tome 61, p.257.

J.~Neuberg. -- M. 1881. {\em Question propos\'ee} n$^o$ 20, p.31. {\em
Solution de
M.~Brocard et Note de M.~Neuberg}, p.138, 158.

J.~Neuberg et Jerabek. -- M. 1881, p.191--193. {\em Sur un hexagone
\'equilat\'eral}.

E.~Lemoine. -- J.E. 1883 --84. Exercices de Math. \'Elem. [Exercices 19,33].

G.~Boubals. -- J.E. 1885. Question propos\'ee 171.

E.~Vigari\'e. -- J.E. 18881. {\em Sur le centre des parall\`eles et sur les
points de Jerabek}. (Question 171).

Best regards
Sincerely
Paul Yiu