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Descartes on the Unification of Arithmetic, Algebra and Geometry Via the Theory of Proportions

Descartes on the Unification of Arithmetic, Algebra and Geometry Via the Theory of Proportions

Davide Crippa, “Descartes on the Unification of Arithmetic, Algebra and Geometry Via the Theory of Proportions,” Revista Portuguesa de Filosofia 73, no. 3–4 (2017): 1239–58, DOI 10.17990/RPF/2017_73_3_1239.

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Descartes on the Unification of Arithmetic, Algebra and Geometry Via the Theory of Proportions

Type Journal Article
Author Davide Crippa
Rights © 2018 Aletheia - Associação Científica e Cultural | © 2018 Revista Portuguesa de Filosofia
Volume 73
Issue 3-4
Pages 1239-1258
Publication Revista Portuguesa de Filosofia
ISSN 0870-5283; 2183-461X
Date 2017
DOI 10.17990/RPF/2017_73_3_1239
Language English
Abstract In this paper, we explore the role of the theory of proportions in the constitution of Cartesian geometry. Particularly, we intend to show that Descartes used it in an essential way to achieve a unification between geometry and arithmetic. Such a unification occurred mainly by redefining the operation of multiplication in order to include both operations among segments and among numbers. Finally, we question about the significance of Descartes’ algebraic thought. Although the goal of Descartes’ Géométrie is to solve geometric problems, his first readers emphasized the role of algebra as a study of relations.
Date Added 17/01/2018, 17:50:20
Modified 17/01/2018, 19:43:04


  • algebra,
  • Descartes,
  • Euclid,
  • geometry,
  • multiplication,
  • proportion theory,
  • structure


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