# secant line

The (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  $(0,\,0)$  and  $(1,\,1)$,  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 SecantLine 2013-03-22 14:50:34 2013-03-22 14:50:34 Mathprof (13753) Mathprof (13753) 15 Mathprof (13753) Definition msc 51M99 secant secant of the curve secant to the curve curve cubic parabola