Le 'vite parallele' di Girard Desargues e Guarino Guarini, fondatori della moderna scienza della rappresentazione

The “parallel lives” of Girard Desargues and Guarino Guarini, lounders of the modern science of representation. The history of geometries representation, that is to say of the science which teaches how to represent a three-dimensional body on a flat sheet of paper, to work it using drawing tools, as the hammer and chisel work stone, is characterised by the constant dichotomy between art and science, that is to say between studies which aim solely at achieving an aesthetic result and those which aim solely at an abstract logical result. From this viewpoint, artists, those whom Desargues called "les practiciens" are always clashing with mathematicians. The former renounce the difficult paths of pure reasoning, while the latter refuse to realise their theories on an operative reality. The extent to which this gap has hampered the progress of the sciences can been estimated better than us by Percy Bridgman who has dedicated his life to demonstratinf5 how theoretical physics should subject its models to the test of operational verification. However, before him, more precisely in the seventeenth century, two persons of great scientific and moral prestige dealt with this problem, opening the path which has led to the modern conception of the science of representation: we are talking of Gerard Desargues and Guarino Guarini. Sons of the same century, of the same mathematical culture, and closer to each other than may be imaged (we are referring to Guarini's trips to Paris) while nevertheless distant as regards their philosophic and scientific conceptions and also as regards the role with which they are commonly attributed by historians, both of them nonetheless were committed to both pure research and also, and above all, in applied research on the problems of art where this word was not ascribed with any romantic connotations, but more simply the meaning of noble and creative manual activity referred to in Monge's letter. In particular, while Desargues takes the credit for the considerable developments in perspective science, which opened the way to Poncelet, Guarini should be credited, we believe, with the first systematic treatment of the method of orthogonal projections, which makes him the most authoritative predecessor of Monge as Chasles himself acknowledged. This article aims at illustrating, albeit in a minimal part and in summary form, Guarino Guarini's contribution so as to shed more light on the role of the seventeenth century mathematicians and hence also Desargues in founding the modern science of representation.