Guarino Guarini and Universal Mathematics

Abstract

Abstract. Guarini considered the mathematical studies to be of fundamental importance for all artists and scholars. His own knowledge of mathematics was vast and profound. The aim of this present paper is to show, through an analysis of the most substantial of his mathematical works, Euclides adauctus, along with the Appendix to this printed a few months later, the role that philosophical and mathematical studies had on his cultural formation, on the new and original research that he conducted, and on his teaching activities, while looking for traces of the mathematical sources that he consulted and cited that indicate which authors and works exerted the greatest influence on him. IntroductionGuarino Guarini, in the dedication to Charles Immanuel II of Savoy of his most important scientific treatise, Euclides adauctus et methodicus mathematicaque universalis, printed in Torino in 1671, underlines the miraculous power that mathematics exerts on architecture, declaring that it is possible to draw on mathematics' most sublime ideas, a science that he sought to enrich with the fruits of his labour:...but above all it is architecture that shines thanks to the distinguished and truly regal Thaumaturgy of the miracles of mathematics. ... Hereby receive, your Royal Highness, with benign visage and serene clemency, that which several times with the breadth of its ingeniousness in conceiving the most sublime ideas has fostered mathematics and all of the efforts of my work in adorning it. Guarini's predilection for mathematics over all other disciplines of learning is expressed more than once. It manifests itself concretely in his artistic creations, which make visible the beauty and harmony of forms born from his love of plane and solid geometry (cf. [Roero 2001]).In his first work of a philosophical-scientific nature, Placita Philosophica ( fig. 1), published in Paris in 1665, he upholds the importance of the knowledge of mathematics for all artists and scholars:All the arts depend on either mathematics, philosophy or medicine, all sciences that examine similitude, proportion or the fittingness of things ... Thus, the more profound the artist's knowledge is regarding the things relative to his art, of the means and manners of applying them, the more excellent will he be judged, and the more perfect his works will be considered. In fact, when the artist sets himself to his task, he does well to choose the most suitable material, to have a perfect knowledge of his instruments, and the ties with all the things relative to the art, and finally to eliminate the devices used to create each thing. And since in the most difficult situations neither imagination nor intellect is sufficient, the devices drawn from these models can be applied most perfectly to the idea to be demonstrated and performed in that particular circumstance. In his final work, Architettura Civile, published posthumously in 1737 under the direction of Bernardo Vittone, Guarini explicitly states architecture's dependence on mathematics:Of the, we might say, ...