In La nova scientia , 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. (shrink)

In his 1551 Travagliata invenzione, the Italian mathematician Niccolò Tartaglia described a device for raising sunken ships. Despite his claim of originality, his contemporary Girolamo Cardano had described a similar method in his famous work De subtilitate, which was published a year before. A comparison between these methods reveals the uniqueness of Tartaglia's approach, for he combines an explicit defence of the horror vacui principle with an implicit negation of rarefaction. In this article I show the complexities of this conception (...) and stress the importance of keeping the personal argument between both authors in mind when interpreting their descriptions of wreck-salvage operations. (shrink)