Geometry, Ordinality, Cardinality

Perhaps the most significant feature of Cartesian Geometry is the introduction of an Origin into Space.  Thus, for example, the priority of Ordinal Numbers over Cardinal Numbers is thereby illustrated.  For, with that innovation, Space is rendered oriented with respect to it, i. e. along a line emerging from the Origin, distinguishable are the point nearest to it, from the point next nearest, from the next point, etc.  Or, numerically expressed, they can be characterized as the first point, the second point, the third point, etc, i. e. expressed as Ordinal Numbers, on the basis of which the Cardinals, i. e. 1, 2, 3, etc., can be derived.  But, the converse is not possible.  For, as is clear in Platonism, The One, The Two, The Three, etc. are mutually discrete, and, hence, are as non-ordered with respect to one another as are the Triangle and the Square.  In other words, Cartesian Geometry illustrates how the sequence of Numbers, qua sequence, is essentially Ordinal, even as they are commonly abbreviated as Cardinal.