Leibniz's Manuscripts on Perspective

In 1677, Leibniz wrote his first essay about geometric characteristic, a new geometry of situation and space, without magnitudes, figures or quantities. Although it is mathematically and philosophically central, the geometry of situations is nonetheless not so accurately known, because of the lack of the editions of it, during Leibniz's life and after it. However, the published texts of the Analysis Situs between 1676 and 1682, in the French edition and translation of J. Echeverría and M. Parmentier in 1995, reveal that its invention could be connected to Leibniz's discovery of the perspective works of Pascal and Desargues. The issue is then to determine the nature of the relation between perspective and geometric characteristic, in order to clarify the true origin of the Leibnizian invention, to define the nature of that space presented as the object of the new geometry, and to decide wether perspective is for Leibniz a "particular example" of a more general science, or a "general model" for more particular geometrical specimen. This last question becomes really problematic when we consider that Leibniz himself wrote some texts about perspective. This set of six mansucritps conserved at the Leibniz-Archiv in Hannover (which are almost all in latin and present a compact and crossed out texts with annotated margins and drawn shapes) is totally unpublished, except for a transcribed paragraph (by J. Echeverría). However, we suppose they might contain some answers to the previous questions and perhaps even some other important elements to shed light on Leibniz's general theory of geometry. Then, my purpose is, first, to develop the reasons why the understanding of the published texts of the Leibniz's invention of the geometry of situations necessarily requires the reading of the manuscripts of perspective. Secondly, I will present the relationship between this reading and a possible new understanding of Leibnizian mathematics as well as of Leibnizian metaphysics, since geometry and perspective play a central role in the general Leibnizian doctrine. Third, I will conclude by exposing the theorical and methodological conditions of a possible transcription of these uneasily readable mansucripts