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 .