Optical Diagrams as “Paper Tools”: Della Porta’s Analysis of Biconvex Lenses from De refractione to De telescopio

In the last decades, the epistemic relevance of mediation and representation strategies in the construction of scientific knowledge has been demonstrated by a large number of studies. Words, symbols, formulas or diagrams on a page provide an essential and epistemically independent means to connect, reflect and expand instrumental and laboratory experience. Historian of science Ursula Klein has introduced the term "paper tool" to describe this kind of function in the case of early chemical formulas, and in the present contribution I will argue that optical ray-tracing diagrams acted as "paper tools" in Della Porta's optical writings. Thanks to diagrammatic practices, Della Porta was able to extend to lenses the connection between light focusing properties and visually perceivable effects that had been recently established for convex mirrors. At the core of the connection stood the ambiguous concept of "point of inversion", and in the present paper we shall follow Della Porta's innovative attempts of adapting it from reflecting to refracting systems using diagrams as paper tools.