Secant line

Common lines and line segments on a circle, including a secant

In geometry, a secant of a curve is a line that (locally) intersects two points on the curve.^[1] A chord is the interval of a secant that lies between the points at which it intersects the curve.^[2] The word secant comes from the Latin word secare, meaning to cut.^[3]

A secant may be used to approximate the tangent to a curve, at some point P. If the secant to a curve is defined by two points, P and Q, with P fixed and Q variable, as Q approaches P along the curve, the direction of the secant approaches that of the tangent at P (assuming that the first derivative of the curve is continuous at point P so that there is only one tangent).^[1] As a consequence, one could say that the limit, as Q approaches P, of the secant's slope, or direction, is that of the tangent. In calculus, this idea is the basis of the geometric definition of the derivative.

See also

• Elliptic curve, a curve for which every secant has a third point of intersection, from which a group law may be defined
• Quadrisecant, a line that intersects four points of a curve
• Secant plane, the three-dimensional equivalent of a secant line

References

External links

• Weisstein, Eric W. "Secant line". MathWorld.