  The phase coexistence is illuminated with geometric views of the
thermodynamic variables, according to Gibbs' choices. Quantities and relations
between them are obtained. The existence of the edge of regression with
tangents coincident with the straight lines connecting the coexistence points
of phase equilibrium is stressed. A geometric approach to the critical point
leads to estimation of the values of the critical exponents for the angles
formed by the coexistence curve and the straight lines with the principal
direction along the minimal curvature.
