Laguerre sowed the seeds for much of the material of this chapter in Sur La Géométrie de Direction . The specific approach we shall be taking is, however, quite different from the approach in the original, or even subsequent, publications of Laguerre. In Chapter 3, much of this material is redeveloped in the Minkowski model. The results of the present chapter are much less mysterious in that context.I don't recall having ever seen, in a paper, this close an equivalent of a professor's usual reassurance that "this will all make sense later."
Source: Robert Knight's 2000 doctoral dissertation "Using Laguerre Geometry to Discover Euclidean Theorems."