Antički korijeni Getaldićeva rada na razvoju matematičke analize i sinteze

Abstract

The diverse opus of Marin Getaldić can methodologically and conceptually be divided into two parts. Getaldić’s early works can be considered as a reinterpretation of selected works from the ancient Greek and Roman tradition with the aim of transmitting ancient knowledge and theories, but also as an effort to further explore and improve these teachings within the framework of ancient Greek mathematical methods. In his more mature works, Getaldić was focused on the problem of the method. For twenty years, in his native Dubrovnik, he was developing the ideas he had encountered on a study trip across Europe, independently and almost completely isolated from the intense developments in the European scientific community in the first decades of the 17th century. He summarized the findings of his research in a seminal, five-volume work De resolutione et compositione mathematica (Rome 1630). Although Getaldić operated in an environment that was permeated by the Renaissance and humanist influences, in his local environment knowledge was transferred more slowly than in Western European countries where modern science emerged during the 16th and 17th centuries. In Dubrovnik isolation, he created new theoretical and practical knowledge, as well as original works that echoed in the European scientific community not only during his lifetime, but also later, during the 17th and 18th centuries. His example shows that the transfer of knowledge did not take place only from European epistemological centers to the periphery, for it shows that the scientific transfers within Europe went in both directions. He worked at a time when the accumulated knowledge about ancient works and the spread of humanistic education outgrew the ancient tradition, and gradually, after the methodological transformation, modern science was founded and shaped. It took almost twenty centuries for the ancient mathematical methodology, complemented by knowledge assimilated from the Arab and Indian mathematical traditions, to be conceptually modified and new methods aiming at achieving new theoretical knowledge and practical solutions to be developed. In building his rich opus, Getaldić relied heavily on the original ancient mathematical methods, which he consistently applied to a variety of problems. His work was largely based on the works of Greek mathematicians, among whom Pappus and Diophantus stand out, and was influenced by Eudoxus’ theory of scale and Archimedes’ application of logical methodology, i.e. arithmetic interpretation of geometry. Getaldić combined different tendencies of ancient Greek mathematics in a unique and fruitful way. After mastering Viète’s symbolic algebra that operated with general quantities, Getaldić systematically explored the possibilities of symbolic algebra in relation to ancient mathematical methods, which played a crucial role in the further development of modern mathematics and gradually lead to another major conceptual change in mathematical history. The change did not only affect mathematics, but also enabled the emergence of new, simpler and more exact interpretations in other sciences as well.