1. the plane that contains all the lines tangent to a specific point on a surface;

The Collaborative International Dictionary of English v.0.48:

Tangent \Tan"gent\, a. [L. tangens, -entis, p. pr.] Touching; touching at a single point; specifically (Geom.) 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. [1913 Webster] Tangent plane (Geom.), a plane which touches a surface in a point or line. Tangent scale (Gun.), a kind of breech sight for a cannon. Tangent screw (Mach.), an endless screw; a worm. [1913 Webster] [1913 Webster]WordNet (r) 3.0 (2006):

tangent plane n 1: the plane that contains all the lines tangent to a specific point on a surface