Eubank and Hall have recently shown the equal area rule (EAR) applies to the composition derivative of the Gibbs energy of a binary system at fixed pressure and temperature regardless of derivative continuity. A sufficient condition for equilibria, EAR is faster and simpler than either the familiar tangent-line method or the area method of Eubank et al. Here, we show that EAR can be extended to ternary systems exhibiting one, two, or three phases at equilibrium. A single directional vector is searched in composition space; at equilibrium, this vector is the familiar tie line. A sensitive criterion for equilibrium under EAR is equality of orthogonal derivatives such as (partial derivative g/partial derivative x(1))(x2P,T) at the end points (alpha and beta), where g = (Delta(m)G/RT). Repeated use of the binary algorithm published in the first reference allows rapid, simple solution of ternary problems, even with hand-held calculators for cases where the background model is simple (e.g., activity coefficient models) and the derivative continuous.