The techniques used, in this paper, are based on the exterior calculus of Maurer-Cartan forms, and Weingarten surfaces are used to illustrate the methods that apply to quadratic exterior equations with constant coefficients. Isothermic surfaces of constant astigmatism (non-linear Weingarten surfaces whose difference of principal curvatures is a constant) are shown to represent dual surfaces of isothermic surfaces which satisfy the relation

Weingarten surface, linear Weingarten surface, Cartan’s moving frame method, isothermic coordinates, dual surfaces.