As mentioned above, oriented spheres in R can be represented by points of four-dimensional space R using minimal (isotropy) projection, which became particularly important in Laguerre's geometry. For instance, E. Müller (1898) based his discussion of oriented spheres on the fact that they can be mapped upon the points of a plane manifold of four dimensions (which he likened to Fiedler's "cyclography" from 1882). He systematically compared the transformations by reciprocal radii (calling it "inversion at a sphere") with the transformations by reciprocal directions (calling it "inversion at a plane sphere complex"). Following Müller's paper, Smith (1900) discussed Laguerre's transformation and the related "group of the geometry of reciprocal directions". Alluding to Klein's (1893) treatment of minimal projection, he pointed out that this group "is simply isomorphic with the group of all displacements and symmetry transformations in space of four dimensions". Smith obtained the same transformation as Laguerre and Darboux in different notation, calling it "inversion into a spherical complex":