The thesis explores a concept or rather a figure, that of horizontality, in its relations with the contemporary urbanized space and the paradigms of its design. It does so by acknowledging the constructive role of figures of speech and metaphors in spatial thinking, not only for their rhetorical value but also for their capacity to suggest forms, ways of physically organizing urban materials in the territory. At the center of my interest are, on the one hand, the "city-territory" - a diffuse form of urbanity that, while not resembling the configurations of the great metropolises of the 19th and 20th centuries, characterizes a large part of contemporary urbanization in Europe and beyond - and, on the other hand, its disciplinary urban traditions, namely theories and projects that in history have explored its forms and potentials. Through a genealogical reading that moves through both contemporary space and the urban discourses surrounding it, the thesis aims at questioning the predominant spatial centered/hierarchical paradigm pervasively rooted in the tradition of western urban design; exploring non-hierarchical conditions of order, dynamic forms of equilibrium, and horizontal relations in space, it is indeed the hypothesis of this thesis that another paradigm already exists in the folds of disciplinary discourse, and that it should be today reclaimed and better explained, being it pertinent and relevant to reflect on the future of urbanized territories. The main objective is thus to contribute outlining such a tradition, looking at the occasions and the ways in which the figure has been employed or has left traces in the disciplinary history of urbanism. The research is organized in two parts, in the form of a genealogical reading: the first explores the emergence of the figure in contemporary territories and the reasons for its topicality, through deepening the meanings of the notion in relations with contemporary urbanization dynamics; the second investigates the presence of the figure in the discourses of architects and urbanist starting from official histories of urbanism. A series of journeys punctuates the two parts, proposing deep readings of specific territories, projects, or theories, to clarify the connections of my investigation with the contemporary urban debates and relate my readings with the challenges the project for city-territory raises. Deconstructing the figure of horizontality and exploring forms of horizontal spatial order in relation to the city-territory contribute in this work to question the approach to contemporary urban design at its epistemological and ontological foundations. This thesis contributes therefore to overcome the opposition compact/dispersed focusing rather on the binomial centered/a-centered, while clarifying the interest of assuming more complex forms of order in spatial thinking to address future research.