This study describes the morphological urban order underlying Portuguese treatises and Portuguese urban cartographic representation produced from 16th century to 18th century. The historical documentation suggests that Pythagorean-Euclidian geometry appears to be a crucial ingredient for the understanding of Portuguese urban design-thinking and urban design-making. To unveil the genesis of the morphological urban order present in the Portuguese colonial plans of the eighteenth century, a descriptive method, Shape Grammar has been adopted. Shape Grammar, as method, supports the analysis of the form-making logic and has proved to be powerful in shape analysis, description, interpretation, classification, evaluation and generation of a design language.