  A novel mathematical rigorous method to obtain the vapor-liquid equilibrium
curves near the critical point has been proposed covering the cases of
well-known and commonly used equations of state for real gases - Van der Waals
and Dieterici, which are prototypes to determine the critical exponent value of
the coexistence curves system. We explain that the critical exponent value of
the vapor-liquid equilibrium curves can be regarded as the analogy to the
results based on classical assumptions - mean field theory. The novelty of our
method has been exposed in comparison to the standard thermodynamic limit
discussed thoroughly and extensively in the literature.
