Pythagorean reforms: * see Endnote 67

Classical number was primal & linked to animate man, the physical body & its organic processes (gender, sex, propagation).  Irrational number threatened this.  An act of control, conjuring, and ‘symbolizing extension’ (Spengler’s terms) was to link Number with religion.  The most basic, organic of all Greek religions were the Eleusinian mysteries.  Spengler sees a conscious link between the Pythagorean Brotherhood & these mysteries as reflected in the rules (reforms) of the Brotherhood which (he suggests) were based on the Eleusinian mysteries.  This is the cult of Demeter, the female agrarian cult, oldest of the cults, spanning almost 2000 years, rooted in Mycenaean traditions (1500 BC).  Originated in Eleusis (in Attica near Athens) story centers on Demeter, the goddess of agriculture, and her daughter Persephone.

 

Polis:

ancient Greek name for city, refers to the ancient Greek city-states (Classical Athens or Sparta). . These cities consisted of a fortified city centre built on an acropolis or harbour and controlled surrounding territories.  They developed during the Archaic period.  They were political entities ruled by their citizens.  The term came to mean state (which included its surrounding villages) and described the entire body of citizens.

 
parallel axiom:

(aka Euclid's 5th postulate) states that in 2-dimensional geometry,  if a line segment intersects two straight lines forming two interior angles on the same side that sum to less than two right angles, then the two lines, if extended indefinitely, meet on that side on which the angles sum to less than two right angles.