affine geometry

As an alternative to the axiomatic approach, affine geometry can be studied via the properties of affine transformations, which do not, in general, preserve distances or angles, but do preserve alignment of points and parallelism of lines.

This chapter is devoted to the theory of affine geometries: those incidence geometries which satisfy the Euclidean parallel postulate in Playfair's form (Ch. 2, Sec. 2).