The natures of numbers in and around Bombelli's L'algebra

Abstract

The purpose of this text is to analyse the mathematical practices leading to Rafael Bombelli's L'algebra (1572). The context for the analysis is the Italian algebra practiced by abbacus masters and Renaissance mathematicians of the 14th-16th centuries. We will focus here on the semiotic aspects of algebraic practices and on the organisation of knowledge. Our purpose is to show how symbols that stand for underdetermined meanings combine with shifting principles of organisation to change the character of algebra.