A secant line of a curve is a line that (locally) intersects two points on the curve. The word secant comes from the Latin secare, to cut.
It can 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. A chord is the portion of a secant that lies within the curve.
A secant line on a map is a line where the projection is without distortion.
Famous quotes containing the word line:
“The real dividing line between early childhood and middle childhood is not between the fifth year and the sixth year—it is more nearly when children are about seven or eight, moving on toward nine. Building the barrier at six has no psychological basis. It has come about only from the historic-economic-political fact that the age of six is when we provide schools for all.”
—James L. Hymes, Jr. (20th century)