Geometry, Ordinality, Space

Kant misses an opportunity to Ordinally ground not only Mathematics, previously discussed, but Geometry, as well.  As is the case with his treatment of Mathematics, his concept of Geometry is standard--Pythagorean-Euclidean--and its connection to his concept of Intuition is only via vague allusion.  However, an alternative derivation begins with one of the prominent innovations of the era--Cartesian Analytic Geometry--and its representation as a centered grid from which arrowed axes emanate.  From there, it is easy to argue that Geometry is grounded in oriented Space, one of the two Forms of Intuition, according to Kant, on the basis of which can be constructed the Vector alternative to Pythagorean-Euclidean Geometry.  But oriented Space is Ordinal Space.  So, he also misses this Ordinal dimension of Intuition, as well, and implications for Geometry.