In this paper the algebraic solntions for elimination SⅠ, SⅡ,SⅢ and SⅣ by the theory of third order aberations are derived. Equations for elimination aberrations are given in terms of the ratios of obscuration and magnifications of the second ary and tertiary and of the oonio constants of the three mirrors. Checks of the equations by the data of some three mirror systems published in foreign papers give good coincidence.