Euler introduced the term affine (Latin affinis, "related") in 1748 in his book "Introductio in analysin infinitorum."

Felix Klein's Erlangen program recognized affine geometry as a generalization of Euclidean geometry.

M. J. Kallaher has written:

'Affine planes with transitive collineation groups' -- subject(s): Affine Geometry, Collineation

In ordinary geometry (as opposed to affine geometry), a plane MUST consist of an infinite set of points.

In the branch of mathematics called differential geometry, an affine connection is a geometrical object on a smooth manifold which connects nearby tangent spaces, and so permits tangent vector fields to be differentiated as if they were functions on the manifold with values in a fixed vector space.

An affine group is the group of all affine transformations of a finite-dimensional vector space.