secant line

The secant line (or simply the secant) of a curve is a straight line intersecting the curve in at least two distinct points.  [The name is initially a participial form of the Latin verb secare ‘’.]

If one sets a secant e.g. to the “cubic parabola”  $y=x^3$  through its points  $(0,\mathrm{\hspace{0.17em}0})$  and  $(1,\mathrm{\hspace{0.17em}1})$,  there is also a third common point  $(-1,-1)$.

Notice that a secant line can also be tangent to the curve at some point, given that tangency is only a local property.  In the following picture, $l$ is a secant line for the curve $C$ (since it intersects the curve at points $A$ and $B$), yet it is also a tangent line at the point $A$.

Title	secant line
Canonical name	SecantLine
Date of creation	2013-03-22 14:50:34
Last modified on	2013-03-22 14:50:34
Owner	Mathprof (13753)
Last modified by	Mathprof (13753)
Numerical id	15
Author	Mathprof (13753)
Entry type	Definition
Classification	msc 51M99
Synonym	secant
Synonym	secant of the curve
Synonym	secant to the curve
Related topic	curve
Defines	cubic parabola