Tangent v. t. : A tangent line curve, or surface; specifically, that portion of the straight line tangent to a curve that is between the point of tangency and a given line, the given line being, for example, the axis of abscissas, or a radius of a circle produced. See Trigonometrical function, under Function.

Tangent a. : Touching; touching at a single point

Tangent a. : meeting a curve or surface at a point and having at that point the same direction as the curve or surface; -- said of a straight line, curve, or surface; as, a line tangent to a curve; a curve tangent to a surface; tangent surfaces.

Example:
How to find the derivative from Tangent lines?

Taxonomy
tangent, tangent line, curve, graph, slope, the origin, passing, derivatives, tangent function, straight line, difference quotient, tangent plane, vertex, touches, slope formula, graph of a function, free encyclopedia, point of tangency.

Defination from the web:
tangent line is "going in the same direction" as the curve, and in this sense it is the best ... Similarly, the tangent plane to a surface at a given point is the plane that "just touches" the surface at that point. ...