In geometry, the subtangent and related terms are certain line segments defined using the line tangent to a curve at a given point and the coordinate axes.
The terms are somewhat archaic today but were in common use until the early part of the 20th century.
Draw the tangent to the curve at P and let T be the point where this line intersects the x-axis.
Then TA is defined to be the subtangent at P. Similarly, if normal to the curve at P intersects the x-axis at N then AN is called the subnormal.
Then So the subtangent is and the subnormal is The normal is given by and the tangent is given by Let P = (r, θ) be a point on a given curve defined by polar coordinates and let O denote the origin.
Subtangent and related concepts for a curve (
black
) at a given point
P
. The tangent and normal lines are shown in
green
and
blue
respectively. The distances shown are the
ordinate
(
AP
),
tangent
(
TP
),
subtangent
(
TA
),
normal
(
PN
), and
subnormal
(
AN
). The angle φ is the angle of inclination of the tangent line or the tangential angle.
Polar subtangent and related concepts for a curve (
black
) at a given point
P
. The tangent and normal lines are shown in
green
and
blue
respectively. The distances shown are the
radius
(
OP
),
polar subtangent
(
OT
), and
polar subnormal
(
ON
). The angle θ is the radial angle and the angle ψ of inclination of the tangent to the radius or the polar tangential angle.
