An effective algorithm is proposed for solving the structure of thin-l
ens cemented triplets which consist of three different glass types and
have the given target values of power, primary spherical aberration,
coma and longitudinal chromatic aberration. The formulae for the aberr
ations are combined with the power formula into a fifth-order polynomi
al equation in one variable, whose roots can all be solved by a combin
ation of numerical and algebraic methods.