THE TORTUOUS WAYS TOWARD A NEW UNDERSTANDING OF ALGEBRA IN THE ITALIAN ABBACUS SCHOOL (14TH–16TH CENTURIES)

different from what we know from al-Khwārizmī and Fibonacci. Indeed, early Modern algebra did not build on these: its foundation was the algebra of the Italian Abbacus school. The paper follows the development of this tradition from 1307 onward, in particular the appearance of abbreviations, the naming of powers and roots, formal calculations, schemes, and the solution of higher-degree equations. THE TRANSFORMATION Ancient Babylonian and Ancient Egyptian mathematics were powerful calculational tools for the solution of scribal tasks- accounting, planning of resources, measurement of land; they were developed and taught for that purpose. What else was achieved by them – e.g., the impressive feats of Old Babylonian “Algebra ” – was derivative and secondary to that purpose. Classical Ancient mathematics had many components:1 • “Practical mathematics ” of the scribal kind. • “Liberal-Arts”-mathematics, the kind of mathematics which a well-bre