Euclid makes several references to the tangent (ἐφαπτομένη ephaptoménē) to a circle in book III of the Elements (c. 300 BC). In Apollonius' work Conics (c. 225 BC) he defines a tangent as being a line such that no other … See more

The intuitive notion that a tangent line "touches" a curve can be made more explicit by considering the sequence of straight lines (secant lines) passing through two points, A and B, those that lie on the function curve. The tangent at A is the limit when point … See more

The tangent plane to a surface at a given point p is defined in an analogous way to the tangent line in the case of curves. It is the best approximation of the surface by a plane at p, and can be obtained as the limiting position of the planes passing through 3 distinct … See more

• Newton's method
• Normal (geometry)
• Osculating circle See more

Two circles of non-equal radius, both in the same plane, are said to be tangent to each other if they meet at only one point. Equivalently, two circles, with radii of ri and centers at (xi, yi), for i = 1, 2 are said to be tangent to each other if
• Two … See more

More generally, there is a k-dimensional tangent space at each point of a k-dimensional manifold in the n-dimensional Euclidean space See more

• J. Edwards (1892). Differential Calculus. London: MacMillan and Co. pp. 143 ff. See more