[21] Hermann Grassmann, one of the founders of modern mathematics, has
called attention to the fact that Euclid had a clearer conception of the
fundamental concepts of mathematics than his ill-informed translators
and interpreters. Grassmann says in his _Ausdehnungslehre_: “From the
imputation of confounding axioms with assumed concepts Euclid himself,
however, is free, Euclid incorporated the former among his postulates
(αἰτήματα) while he separated the latter as common concepts (κοιναὶ
ἐννοιαι)—a proceeding which even on the part of his commentators was no
longer understood, and likewise with modern mathematicians, unfortunately
for science, has met with little imitation. As a matter of fact, the
abstract methods of mathematical science know no axioms at all.”—Quoted
from _The Open Court_, Vol. II. No. 77, _A Flaw in the Foundation of
Geometry_, by Hermann Grassmann, translated from his _Ausdehnungslehre_
by μκρκ.