  In this communication, the derivation of the Boltzmann-Gibbs and the
Maxwellian distributions is presented from a geometrical point of view under
the hypothesis of equiprobability. It is shown that both distributions can be
obtained by working out the properties of the volume or the surface of the
respective geometries delimited in phase space by an additive constraint. That
is, the asymptotic equilibrium distributions in the thermodynamic limit are
independent of considering open or closed homogeneous statistical systems.
