  We write explicitly the Euler identity and the Gibbs-Duhem relation for
thermodynamic potentials that are not homogeneous first-order functions of
their natural extensive variables. We apply the rules to the theory of
geometrothermodynamics and show how the use of the natural extensive variables,
instead of the modified ones, leads to misleading results. We further reveal
some other ambiguities and inconsistencies in the theory and we make new
suggestions.
