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The techniques used in this paper are based on the exterior calculus ofMaurer-Cartan forms, and Weingarten surfaces are used to illustrate the methodsthat apply to quadratic exterior equations with constant coefficients.Isothermic {\it surfaces of constant astigmatism} (non-linear Weingartensurfaces whose difference of principal curvatures is a constant) are shown torepresent dual surfaces of isothermic surfaces which satisfy the relation $H +\alpha K = 0$.

Weingarten surfaces with moving frames -- a tribute to S.S. Chern and C.L. Terng -- and a duality result