Nicla Palladino

TL;DR: In this paper, the authors document the history of the models of mathematical surfaces used for the didactics of pure and applied "High Mathematics" in Italy and in Europe, between the second half of the nineteenth century and the 1930s.

TL;DR: Palladino et al. as mentioned in this paper presented a general catalogue and the website of the mathematical models found in the Italian universities of Catania, Messina, Bari, Naples, Rome, Florence, Bologna, Modena, Ferrara, Parma, Pavia, Milan, Padua, Turin and Genoa.

Abstract: In this paper we develop some relationships between the approximation method Rafael Bombelli used to find the square root of an integer number in his Algebra (1572), Leibniz’s “hidden calculus” in infinitesimal algorithms (Nova Methodus, 1684) and Newton’s procedures of extraction more arithmetico of the root of a binomial: these procedures lead to the series development of a binomial root that Newton used in integral calculus (ca. 1666). Riassunto: Nell’articolo, vengono confrontati alcuni procedimenti di approssimazione, dovuti a Rafael Bombelli per calcolare la radice quadrata di un numero (Algebra, 1572) con il “calcolo nascosto” degli algoritmi infinitesimali di Leibniz (Nova Methodus, 1684) e, ancora, con procedure per l’estrazione della radice di un binomio concepite da Newton: queste ultime conducono agli sviluppi in serie di binomi che Newton adoperò per il calcolo integrale. 1. THE SQUARE ROOT AND METHODS OF APPROXIMATION. It is possible to find direct and recursive methods for calculating square roots of integer numbers since the second century. Bombelli, in his Algebra, and Newton, in Arithmetica Universalis, exposed Claudius Ptolemy’s method that has been used for calculating both exact and nonexact square roots. Newton proposed a graphic scheme (“a danda lunga”, which means all passages included) for calculating the square root following Ptolemy’s method. The extraction of the square root of 22178791 is one of the two examples given by Newton [Newton 1707, pp. 32-33]: I Trav. Ianniello, 7. Frattamaggiore (NA). E-mail: nicla.palladino@unina.it 1 Ptolemy’s method is nearly equal to methods that we can read nowadays in arithmetic manuals for the first level middle school.