L'insegnamento dell'aritmetica nel "General Trattato" di Niccolò Tartaglia

In 1542 Tartaglia begun writing the General Trattato di numeri et misure, a work directed to overshadow the famous Pacioli’s Summa. Before his death, in 1557, he was able to publish only the First and the Second Part devoted to arithmetic (the remaining Parts being published posthumously in 1560). This paper analyzes the First and Second Part, comparing especially Tartaglia’s and Pacioli’s arithmetical approach and showing how Tartaglia was definitely oriented towards algebra even if he was very careful in using correctly algebraic tools. In this work emerge two of Tartaglia’s “souls” and they appear strictly connected, that is the “abacus teacher” and the “translator of Classics”. The teacher is particularly interested in solving problems and in techniques of fast mental calculation, whereas the translator pays attention to the semantic ambiguity hidden in the common language. The aim of this paper is sheding a new light on both Tartaglia’s scientific thought and the teaching of mathematics in the Renaissance.