 The status of the straight line in elementary Euclidean geometry as both the shortest curve joining any two of its points and as the curve that points always in the same direction was disentangled. One line of enquiry led to geometries that emphasised straightness as the fundamental property (typically, projective geometry) and the other to geometries that emphasised the shortest aspect. The former approach was seen from the start as a non-metrical one, and became the favoured arena for formal, even axiomatic investigations of geometry as a deductive enterprise. The price was having less and less to say about physical space (as Poincaré observed). The concept of geometry was radically enlarged, but in ways that were not intended to be accounts of physical space or experiential space.