Paolo Palmieri
University of Pittsburgh
Bonaventura Cavalieri has been the subject of numerous scholarly publications. Recent students of Cavalieri have placed his geometry of indivisibles in the context of early modern mathematics, emphasizing the role of new geometrical objects, such as, for example, linear and plane indivisibles. In this paper, I will complement this recent trend by focusing on how Cavalieri manipulates geometrical objects. In particular, I will investigate one fundamental activity, namely, superposition of geometrical objects. In Cavalieri’s practice, superposition is a means of both manipulating geometrical objects and drawing inferences. Finally, I will suggest that an integrated approach, namely, one which strives to understand both objects and activities, can illuminate the history of mathematics.
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DOI 10.1007/s00407-008-0032-z
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References found in this work BETA

Philosophy of Mathematics and Deductive Structure of Euclid 's "Elements".Ian Mueller - 1983 - British Journal for the Philosophy of Science 34 (1):57-70.
Cavalieri's Method of Indivisibles.Kirsti Andersen - 1985 - Archive for History of Exact Sciences 31 (4):291-367.

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On the Relationship Between Plane and Solid Geometry.Andrew Arana & Paolo Mancosu - 2012 - Review of Symbolic Logic 5 (2):294-353.

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