# Tangent

In geometry, the **tangent line** (or simply **tangent**) to a plane curve at a given point is the straight line that "just touches" the curve at that point. Leibniz defined it as the line through a pair of infinitely close points on the curve.[1] More precisely, a straight line is said to be a tangent of a curve *y* = *f*(*x*) at a point *x* = *c* if the line passes through the point (*c*, *f*(*c*)) on the curve and has slope *f*'(*c*), where *f*' is the derivative of *f*. A similar definition applies to space curves and curves in *n*-dimensional Euclidean space.

As it passes through the point where the tangent line and the curve meet, called the **point of tangency**, the tangent line is "going in the same direction" as the curve, and is thus the best straight-line approximation to the curve at that point.

The tangent line to a point on a differentiable curve can also be thought of as a *tangent line approximation*, the graph of the affine function that best approximates the original function at the given point.[2]

Similarly, the **tangent plane** to a surface at a given point is the plane that "just touches" the surface at that point. The concept of a tangent is one of the most fundamental notions in differential geometry and has been extensively generalized; .

The word "tangent" comes from the Latin *tangere*, "to touch".