Showing papers in "Bollettino Di Storia Delle Scienze Matematiche in 2010"

Polynomials and equations in medieval italian algebra

Abstract: A recent study (Oaks 2009) shows that the medieval Arabic concepts of polynomial and equation differ from those of modern algebra. We present here a continuation of this study for medieval Italian algebra, and show that Italian abbacus authors possessed essentially the same medieval concepts as their Arabic predecessors. In short, polynomials were regarded as aggregations of the different species (powers) of the unknown, and medieval algebraists preferred to set up polynomial equations devoid of mathematical operations. These concepts are consistent with the various medieval Italian notations, and extended down to Bombelli's time.

Medieval Heritage and New Perspectives in Cardano's Practica arithmetice

Abstract: Practica arithmetice represents a work of transition from different points of view. Concerning Cardano's mathematical corpus, it is the first step of his ambitious arithmetical encyclopedia, the Opus perfectum, whose unique published volume was the famous Ars magna. In the Renaissance mathematics, it marks the passage from the abacus tradition to a more modern approach to algebraic rules, deeper developed in the Ars magna few years later. In this paper we briefly describe the genesis of the Opus perfectum and discuss some algebraic rules contained in the Practica. We focus our attention on the interpretation of the method of the auxiliary unknown provided by Cardano and illustrated by the Regula de duplici and the Regula de medio, inherited by medieval algebra, and the original Regula de modo, suitable to solve a linear system of two equations in two unknowns.

Questioni didattiche e divulgazione scientifica: gli interventi di luigi cremona sull'«effemeride della pubblica istruzione» (1860-1865)

Abstract: Among the great Italian mathematicians of the Risorgimento period, Luigi Cremona (1830-1903) was the one who, in the early years of the Unification of Italy, deeply committed himself in the field of didactics and popularization of scientific theories by personally preparing some of the teaching syllabuses for Italian secondary schools and carrying out an important activity of divulgation of higher mathematics among teachers. His didactic reflections and commitment in popularizing are the object of this paper where we analyse, by setting them in an historical period, some of his minor writings that historians have never considered before, published between 1860 and 1865 on an important Italian educational magazine: l'«Effemeride della pubblica istruzione» («The Ephemeris of State Education»).

L'Asymptote : Apollonius et ses lecteurs.

Abstract: In proposition 14 of the second book of his Conics, Apollonius proves that the asymptotes and the hyperbola approach one another indefinitely without meeting. This proposition appeals to the notion of infinity and of infinite construction of the sequences of distances between the curve and its asymptote. But this notion of 'infinity' was bound to create problems for both mathematicians and philosophers, since Geminus and Proclus. These problems were taken anew by al-Sijzī (second half of 10 th century) and his followers. In this article, the reader will find an outline of the history of this question, an analysis of the work of al-Qummī (a successor of al-Sijzī), as well as a critical edition and translation of new materials concerning the study of asymptotic behaviour.