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 $A$.