A secant line, also simply called a secant, is a line passing through two points of a curve. As the two points are brought together (or, more precisely, as one is
brought towards the other), the secant line tends to a tangent
line.

which is the slope of the line connecting the points and . The limiting value

(2)

as the point
approaches
gives the instantaneous slope of the tangent
line to
at each point ,
which is a quantity known as the derivative of , denoted or .

The use of secant lines to iteratively find the root of a function is known as the
secant method.

In geometry, a secant line commonly refers to a line that intersects a circle at exactly two points (Rhoad et al. 1984, p. 429). There are a number of
interesting theorems related to secant lines.

In the left figure above,

(3)

while in the right figure,

(4)

where
denotes the angular measure of the arc (Jurgensen 1963, pp. 336-337).