Superposition: on Cavalieri's Practice of Mathematics
Arch. Hist. Exact Sci. (2009) 63:471–495 DOI 10.1007/s00407-008-0032-z Superposition: on Cavalieri’s practice of mathematics Paolo Palmieri Received: 22 August 2008 / Published online: 6 November 2008 © Springer-Verlag 2008 Abstract 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 comple- ment this recent trend by focusing on how Cavalieri manipulates geometrical objects. In particular, I will investigate one fundamental activity, namely, superposition of geo- metrical 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. 1 Introduction Bonaventura Cavalieri (1598?–1647) has been the subject of numerous scholarly publications.1 Most students of Cavalieri have placed his geometry of indivisibles Communicated by U. Bottazzini. 1 A number of studies have focused on specific aspects, often on the question of the epistemological status of indivisibles as new mathematical objects on the seventeenth-century scene. Cf., for example, Agostini (1940), Cellini (1966b), Vita (1972), Koyré (1973), Terregino (1980), Terregino (1987)andBeeley (1996, pp. 262–271). Other studies have tackled issues concerning Cavalieri’s biography, for instance, Piola (1844), Favaro (1885); or the genesis of Cavalieri’s Geometry, for example, Arrighi (1973), Giuntini (1985), and Sestini (1996/97).
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