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

0488780 - FLÚ 2018 RIV PT eng J - Journal Article
Crippa, Davide
Descartes on the Unification of Arithmetic, Algebra and Geometry Via the Theory of Proportions.
Revista Portuguesa de Filosofia. Roč. 73, č. 3/4 (2017), s. 1239-1258. ISSN 0870-5283
Institutional support: RVO:67985955
Keywords : algebra * Descartes * Euclid * geometry * multiplication * proportion theory * structure
OECD category: Philosophy, History and Philosophy of science and technology

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.
Permanent Link: http://hdl.handle.net/11104/0283322