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Article ID: CBB001022145

Descartes and the Cylindrical Helix (2010)

Mancosu, Paolo (Author)
Arana, Andrew (Author)

Historia Mathematica
Volume: 37
Pages: 403--427
Publication date: 2010
Language: English

Publication Date: 2010
Edition Details: Part of a special issue, “Contexts, Emergence and Issues of Cartesian Geometry”

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Mathematics Geometry Collected correspondence 17th century France Descartes, René Mersenne, Marin

In correspondence with Mersenne in 1629, Descartes discusses a construction involving a cylinder and what Descartes calls a helice. Mancosu has argued that by helice Descartes was referring to a cylindrical helix. The editors of Mersenne's correspondence (Vol. II), and Henk Bos, have independently argued that, on the contrary, by helice Descartes was referring to the Archimedean spiral. We argue that identifying the helice with the cylindrical helix makes better sense of the text. In the process we take a careful look at constructions of the cylindrical helix available to Descartes and relate them to his criteria for excluding mechanical curves from geometry.

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Article Maronne, Sébastien (2010) Contexts, Emergence and Issues of Cartesian Geometry: In Honour of Henk Bos's 70th Birthday. Historia Mathematica (p. 341). unapi

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