# Secant line

In geometry, a **secant line** of a curve is a line that (locally) intersects two points on the curve.^{[1]}
A chord is an interval of a secant line, the portion of the line that lies within the curve.^{[2]}
The word *secant* comes from the Latin word *secare*, meaning *to cut*.^{[3]}

Secants 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).^{[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

- 1 2 Protter, Murray H.; Protter, Philip E. (1988),
*Calculus with Analytic Geometry*, Jones & Bartlett Learning, p. 62, ISBN 9780867200935. - ↑ Gullberg, Jan (1997),
*Mathematics: From the Birth of Numbers*, W. W. Norton & Company, p. 387, ISBN 9780393040029. - ↑ Redgrove, Herbert Stanley (1913),
*Experimental Mensuration: An Elementary Test-book of Inductive Geometry*, Van Nostrand, p. 167.