Tartaglia's ragioni: A maestro d'abaco's mixed approach to the bombardier's problem

Abstract

AbstractIn La nova scientia (1537), Niccolò Tartaglia analyses trajectories of cannonballs by means of different forms of reasoning, including ‘physical and geometrical reasoning’, ‘demonstrative geometrical reasoning’, ‘Archimedean reasoning’, and ‘algebraic reasoning’. I consider what he understood by each of these methods and how he used them to render the quick succession of a projectile's positions into a single entity that he could explore and explain. I argue that our understanding of his methods and style is greatly enriched by considering the abacus tradition in which he worked. As a maestro d'abaco in sixteenth-century Venice he had access to a great variety of mathematical and natural-philosophical works. This paper traces how Tartaglia drew elements from a vast spectrum of sources and combined them in an innovative manner. I examine his use of algebra and geometry, consider what he knew about Archimedes and suggest a reading of his enigmatic phrase ‘Archimedean reasoning’, which has eluded satisfactory interpretation.