Given a line having trilinear coordinate equation
 |
with respect to a reference triangle 
, the point
 |
is called the trilinear pole of the line with respect to 
(Kimberling 1998, p. 38).
The following table gives the trilinear poles for some named lines.
Let 
be the intercept of the line 
and 
, and let 
be the harmonic conjugate
of 
with respect to 
and 
.
Similarly define 
and 
.
Then 
is the Cevian triangle of the trilinear pole of
.
