There are at least two theorems known as Salmon's theorem. This first states that if 
and 
are two points, 
and 
are the perpendiculars from 
and 
to the polars of 
and 
, respectively, with respect to a circle
with center 
,
then 
(Durell 1928; Salmon 1954, §101, p. 93).
The second Salmon's theorem states that, given a track bounded by two confocal ellipses, if a ball is rolled so that its trajectory is tangent to the inner ellipse, the ball's trajectory will be tangent to the inner ellipse following all subsequent caroms as well (Salmon 1954, §189, pp. 181-182).
