 In the opinion of many in the 19th century, Euclidean geometry lost its fundamental status to a geometry that was regarded as more general: projective geometry. (For an introduction to geometry in the 19th century, see Gray 2011. Projective geometry is described in the entry,  Nineteenth Century Geometry,  see also the essays by various authors in Bioesmat-Martagon 2011.) Projective geometry has its own foundational problem, akin to that of distance in Euclidean geometry, which concerns the concept of cross-ratio, and we need to follow the moves to create projective geometry as an independent subject, to define cross-ratio in this setting, and to resolve the epistemological issues that are raised (an achievement associated with Klein’s Erlangen Programme). We shall also see that the growth of projective geometry creates the arena for Hilbert’s axiomatisation of geometry.