Common tangent

A line tangent to two curves or to a curve at two distinct points. For functions $g_1,g_2$, contact at $x_1,x_2$ requires equal derivatives and equal intercepts: $g_1^{\prime }(x_1)=g_2^{\prime }(x_2)=m$ and $g_1(x_1)-m{x}_1=g_2(x_2)-m{x}_2$. The common-tangent construction uses the lower supporting line for phase coexistence.