ABSTRACT
This chapter examines the visioning techniques in the perspectival and projective geometric methods of Girard Desargues ( Sieur Girard Desargues Lyonnois ; d. 1661). This line of inquiry is undertaken in view of investigating his aims in aiding the construction of architectural space through the mathematical underpinning of its visual representation with greater precision and objectivity. Desargues built on techniques in optical knowledge that he and his contemporaries inherited from the perspectiva traditions of the Italian Renaissance in addition to furthering the development of geometry in its projective modes as an inquiry concerning the invariant properties of figures and solids that are subjected to geometrical transformation, with special attention given to conics and gnomonic projections (the latter dealing with plotting spherical surfaces on a rectilinear plane in geodesic mapping and designing sundials). Desargues undertook these investigations in the context of his scientific research as a geometer and optician besides his technical knowledge as a practicing architect who concentrated on the arts of masonry and stonecutting ( la coupe des pierres ). The projective methods he deployed in establishing his perspective constructions were laid down on geometrical optics and posited a convergence point at infinity that opened up Euclidean space beyond what his predecessors in the Renaissance did in their take on the perspectival costruzione legittima (Brunelleschi, Alberti, etc.). As an architect, Desargues made contributions to rigorous and positive scientific knowledge. His architectural inquiries expanded the realm of understanding natural phenomena through research in the exact sciences and by way of adopting their mathematized epistemic and methodological directives in serving surveyors and engineers to perfect their mensuration.
