Two worshipful illusions about Euclid:

1. belief in Euclid's great axiomatic achievement, whereas an axiom for order was not formulated until 1880 by Moritz Pasch (please see consequence at ordinology.htm);
2. a satisfactory set of axioms for "Euclidean geometry" was not achieved until those of German mathematician, David Hilbert (1862-1943), in 1896, in his Grundlagen der Geometrie;
3. acceptance of Euclid's demonstrations of congruence (the basic equivalence relation in geometry), whereas he allowed demonstration of congruence by moving a figure over and placing it upon another -- which is physics, not mathematics, resulting in circularity, because the physics depended upon the math which depended on physics which .....