Abstract :
In La nova scientia (1537), Niccolo` 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 sixteenthcentury
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.
