Secant line

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

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). 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.

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