The subtangent of a plane curve at a point 
is the directed line
segment on the x-axis from the point where
the tangent line meets the axis to the perpendicular
projection of 
onto the axis. If 
is finite and nonzero, its directed length is
 |
The tangent line meets the x-axis at abscissa 
, so the directed difference from that intercept to 
is 
.
A vertical tangent has zero subtangent. A horizontal tangent at a point with 
has no finite x-axis
intercept, corresponding to an infinite subtangent. The analogous projection
of a normal line segment is the subnormal.
