Note 47 — Introductory material

Now in discussing the systems of Metageometry, we have found two kinds, radically distinct and subject to different axioms. The historically prior kind, which deals with metrical ideas, discusses, to begin with, the conditions of Free Mobility, which is essential to all measurement of space. It finds the analytical expression of these conditions in the existence of a space-constant, or constant measure of curvature, which is equivalent to the homogeneity of space. This is its first axiom.