Tartaglia's ragioni

In 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

Demonstrative · Literal (mathematical logic · Historical and Literary Studies · Historical Philosophy and Science · History and Theory of Mathematics

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  Open Access•Paolo Mancosu•Studies in History and Philosophy…•1992

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  Open Access•Serafina Cuomo•History of Science•1997

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  Mary J Henninger-Vo, Mary J Henninger-Voss•Journal of the History of Ideas•2002

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• The Social Status of Italian Mathematicians, 1450-1600

  Open Access•Mario Biagioli•History of Science•1989

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• Archimedes and the Invention of Artillery and Gunpowder

  D L Simms•Technology and Culture•1987

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• The Scope of Renaissance Mechanics

  W R Laird•Osiris•1986

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• Archimedes among the Humanists

  W R Laird•Isis•1991

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