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Prilozi za istraživanje hrvatske filozofske baštine, Vol. 38. No. 2 (76), 2012.

Original scientific paper

Getaldić , Descartes and Analytical Geometry

Marijana Borić ; Zavod za povijest i filozofiju znanosti HAZU, Zagreb, Hrvatska

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Abstract

The paper examines the mathematical method applied by Marin Getaldić in his main work De resolutione et compositione mathematica (1630), juxtaposing it with the method applied in his earlier works and comparing it to Descartes’s views about the method of scientific research in general. Contrasting Getaldić’s strictly mathematical approach and Descartes’s broader philosophical (and not solely mathematical) approach, one comes to the conclusion that Getaldić, apart from the derived outstanding mathematical results, lacked broader philosophical perspective required for the creation of a new field of mathematics – analytical geometry. It is in this context that the paper aims to evaluate Getaldić’s general contribution to the development of mathematics.
After the first six works written in methods which arise from the tradition of ancient mathematics, Getaldić wrote his most important work De resolutione et compositione mathematica which is completely based on the new Viète’s algebraic method. He consistently and quite generally develops an algebraic method, being aware of the importance of choosing a methodological approach as a major component and driving force in the further development of mathematics. Application of the new method to different problems and theorems of ancient, particularly Euclidean geometry, enabled the reinterpretation of mathematical knowledge and opened the door to new fields of science. Getaldić himself approached yet did not come to the discovery of analytical geometry, but his work is directly involved in the preparation and creation of the seminal synthesis of arithmetic continuum of numbers and geometrical continuum of points, achieved a few years later by Descartes in his La
Géométrie (1637).

Keywords

Marin Getaldić; François Viète; René Descartes; development of mathematics; philosophy; history of science; analysis; synthesis; problem of the method; symbolic algebra; geometric method; algebraic method; analytical geometry

Hrčak ID:

97798

URI

https://hrcak.srce.hr/97798

Publication date:

31.1.2013.

Article data in other languages: croatian

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