Hermann Grassmann Quote

From the imputation of confounding axioms with assumed concepts Euclid himself, however, is free. Euclid incorporated the former among his postulates while he separated the latter as common concepts—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.


As quoted in "Diverse Topics: The Origin of Thought Forms," The Monist (1892) Vol. 2 ed., Paul Carus, citing The Open Court Vol. II. No. 77. A Flaw in the Foundation of Geometry by Hermann Grassmann, translated from his Ausdehnungslehre

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Picture Quote 1

From the imputation of confounding axioms with assumed concepts Euclid himself, however, is free. Euclid incorporated the former among his postulates ...

Picture Quote 2

From the imputation of confounding axioms with assumed concepts Euclid himself, however, is free. Euclid incorporated the former among his postulates ...

Picture Quote 3

From the imputation of confounding axioms with assumed concepts Euclid himself, however, is free. Euclid incorporated the former among his postulates ...

Picture Quote 4

From the imputation of confounding axioms with assumed concepts Euclid himself, however, is free. Euclid incorporated the former among his postulates ...