Secant Line -- From Wolfram MathWorld

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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.

The secant line connects two points and in the Cartesian plane on a curve described by a function . It gives the average rate of change of from to

(1)

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 abstract mathematics, the points connected by a secant line can be either real or complex conjugate imaginary.

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.