Medieval Heritage and New Perspectives in Cardano's Practica arithmetice

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. Recensito da M.R.Massa Esteve in Zentralblatt MATH Database (Zbl 1220.01002) Abstract in MathSciNet (MR2797366 2012a:01010)