Sixty years ago, Friedrich Sanides traced the origin of the tangential expansion of the primate neocortex to two ancestral anlagen in the allocortex of reptiles and mammals, and proposed the Hypothesis on the Dual Origin of the Neocortex. According to Sanides, paraolfactory and parahippocampal gradients of laminar elaboration expanded in evolution by addition of successive concentric rings of gradually different cortical types inside the allocortical ring. Rodents had fewer rings and primates had more rings in the inner part of the cortex. In the present article, we perform cortical type analysis of the neocortex of adult rats, Rhesus macaques, and humans to propose hypotheses on homology of cortical areas applying the principles of the Hypothesis on the Dual Origin of the Neocortex. We show that areas in the outer rings of the neocortex have comparable laminar elaboration in rats and primates, while most 6-layer eulaminate areas in the innermost rings of primate neocortex lack homologous counterparts in rats. We also represent the topological distribution of cortical types in simplified flat maps of the cerebral cortex of monotremes, rats, and primates. Finally, we propose an elaboration of the Hypothesis on the Dual Origin of the Neocortex in the context of modern studies of pallial patterning that integrates the specification of pallial sectors in development of vertebrate embryos. The updated version of the hypothesis of Sanides provides explanation for the emergence of cortical hierarchies in mammals and will guide future research in the phylogenetic origin of neocortical areas.