THE SPATIAL MODELS IN THE TREATISE DE PROSPECTIVA PINGENDI BY PIERO DELLA FRANCESCA

De Prospectiva Pingendi is a Treatise whose destiny is best reflected in the title: a work dedicated to painters, that teaches them the art of illusion. It therefore teaches them to construct an image that evokes the depths of space, passing through walls and painted tablets, to show landscapes, envi-ronments and human figures, seen as we see them in our daily experience of the world. Thus, for centuries, what has attracted the attention of readers and exegetes to this work, was the final result of Piero\u2019s teaching: the prospective or, to better say, the perspective image. Consequently, the Trea-tise has been thoroughly investigated in the context of art history, less in the history of methods of representation. On the occasion of the Italian national print edition which, for the first time, con-templates the Latin and Vernacular manuscripts, as well as all of Piero della Francesca\u2019s original drawings, the treatise has been the object of in-depth analysis and critical review. This review high-lights the two space models Piero mastered permitting the construction of perspective. The first of these models, used in the first and second books, is that of the space as it appears, or as we would say today, the projective space. Piero states the law that describes the compression of this space as a function of the distance by the observer as a succession of magnitudes. This law has an unsuspected generality and alone provides a theoretical support to all subsequent perspective constructions, even in the absence of expedients, such as the distance point, that appears unrelated to Piero della Fran-cesca\u2019s concept. The second model, which is used in the third book, is that of space as it is. This model is not theorized, but only practiced. And yet we can find, in the model, characters that are specific to the method in its full maturity: the presence of associated orthogonal projections, the control of movements in order to handle items in general location and the discretization of the mod-eled forms. Perspective is a bridge between those two conceptions of space and between the ancient and the modern world