Gauss's thorough knowledge of languages would make him likely to
take care in choosing such a technical term. "Congruent" comes from the
verb "congruo," for which a small Latin dictionary gives the meanings "to
run together, coincide, correspond, agree, be consistent with." For
"modulus" it gives "a small measure." So "a is congruent with b modulo
c" could be taken to mean "a corresponds/agrees with b, with respect to
the small measure c." That seems to capture the idea pretty well.
The geometrical use of "congruent" was probably due to Leibniz. I
sent Jeff Miller the details which
http://members.aol.com/jeff570/mathword.html now has.
Ken Pledger.