The name, which goes back to Mobius and Leonhard Euler, implies that, in such a transformation, infinitely distant points correspond again to infinitely distant points, so that, in a sense, the “ends” of space are preserved. In fact, the formulas show at once that x´, y´, z´ become infinite with x, y, z. This is in contrast to the general projective transformations, which we shall study later, in which x´, y´, z´ are fractional linear functions, and by which, therefore, certain finite points will be moved to infinity. These affine transformations play an important role in physics under the name of homogeneous deformations. The word “homogeneous” implies (in contrast to heterogeneous) that the coefficients are independent of the position in space under consideration; the word “deformation” reminds us that, in general, the form of any body will be changed by the transformation.