The synthesis of polysyllogisms in Critical Logic is an important topic within the larger topic of Critical mathematics. My previous treatises have touched upon the logical organization of the manifold of concepts and the manifold of rules in nous, but the levels and scopes of these works are too high and broad to have permitted a detailed exposition of the Logic of structuring series of combined representations in an organized manifold. The aim of this paper is to make a beginning in filling in this omission as one of the early steps in the development of an organon of Critical mathematics and a doctrine of transcendental Logic. A second aim of this paper is to provide a specific illustration of the methodology of doing Critical Logic. Such an illustration is necessary propaedeutic for teaching other scholars how the Critical Theory is applied in general Logic.