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
line at a point with 
has no finite x-axis
intercept, corresponding to an infinite subtangent. At a point
with 
, a horizontal tangent line coincides with the x-axis
and does not determine a unique subtangent. The analogous
projection of a normal
line segment is the subnormal.
