Sunday, July 28, 2019

Line, Vector, Ordinality

In Geometry, a Vector signifies Direction from a point of origin.  But Direction implies Motion.  So, a Vector is often used to represent Motion.  But, more immediately, it exemplifies Motion, i. e. the Motion by which a Line with an arrow affixed is drawn.  Furthermore, all lines are drawn, and drawn from an origin to a terminal point.  Thus, all lines are produced by directed motions.  Hence, all lines are vectors, whether or not they are illustrated as such.  Furthermore, the main elements of Pythagorean-Euclidean Geometry are constructed out of lines--planes and solids.  Now, Direction connotes Order, i. e. the drawing of a Line is ordered from origin to terminus.  Hence, just as Cardinal Numerology is derived from Ordinal Numerology, Pythagorean-Euclidean Geometry is derived from Ordinal Geometry, i. e. Vector Geometry.  The possible priority of the latter is in front of Kant whenever he uses the drawing of a Line as an illustration, but he does not recognize it as such.

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