, etc., without having recourse to terms such as
,
, etc., would of itself imply that the continuum was flat and free from all trace of non-Euclideanism or curvature. Furthermore, it implies that the mesh-system to which we refer this distance is one of straight lines, and is not curvilinear (see [Chapter VII]).
The only flat continuum we have studied so far is the Euclidean one, but in the present case we see that though flat, our continuum is not strictly Euclidean owing to the minus sign preceding
; or, again, owing to the fact that
