This construction, based on f ( v , T ) defined earlier by Gibbs, was originally used by van der Waals (he called it both a double and common tangent), because it could be easily extended to include binary fluid mixtures for which an isotherm of f ( v , x , T ) , with x = N 1 / ( N 1 + N 2 ) a composition variable, forms a surface that can have a common tangent plane. It has subsequently become a popular way to treat phase change problems.