tridimensionality:

Spengler coins a word, meaning 3 dimensions

 

Kant’s greatness: * see Endnote 7

Spengler credits Kant with developing the concept of a priori form (the necessary conclusions from first premises, that which must come before sense observation), but totally dismisses the philosopher’s application of this form to Space and Time.  He is making the case for a relativist conception of reality and one heavily based on solipsism.

​

ratiocination:

the process of logical reasoning

 

non-Euclidean geometry (Gauss):

non-Euclidean geometry consists of 2 geometries based on axioms closely related to those specifying Euclidean geometry. Euclidean geometry lies at the intersection of metric geometry and affine geometry, non-Euclidean geometry arises when either the metric requirement is relaxed, or the parallel postulate is replaced with an alternative one.   Around 1813, Gauss had the germinal ideas of non-Euclidean geometry worked out, but failed to publish. This discovery was a major paradigm shift in mathematics, as it freed mathematicians from the mistaken belief that Euclid's axioms were the only way to make geometry consistent and non-contradictory.

​

and see Chapter II, Numbers, page 67