The Definition of a Tangent to a Curve

1. In elementary geometry, the tangent to a curve C at a point P is defined as the limiting position of the chord PQ as Q tends to P along the curve. Further, C is said to have a continuous tangent at P if it has a tangent at every point Q in the neighbourhood of P, and if the tangent at Q tends to the tangent at P as Q tends to P along C.1