Descartes’ Transformation of Greek Notion of Proportionality

Piotr Błaszczyk ()
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Piotr Błaszczyk: Institute of Mathematics, Pedagogical University of Cracow

A chapter in Handbook of the History and Philosophy of Mathematical Practice, 2024, pp 235-267 from Springer

Abstract: Abstract In ancient Greek mathematics, the general term μέγεϑος stands for geometric magnitudes of all kinds. Euclid’s book V develops a theory of magnitudes, their ratios, and proportions. Viewed from the modern perspective, the theory of proportions is a technique of processing ratios. In early modern mathematics, it was replaced by implicit rules of an ordered field, then, in the nineteenth century, by the arithmetic of real numbers. We formalize Euclid’s theory from book V and show how it was reshaped in Descartes’ La Géométrie.

Keywords: Magnitude; Ratio; Proportion; Algebra of line segments; Arithmetic of line segments; Ordered field; Real closed field; Descartes’ plane (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-40846-5_16

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DOI: 10.1007/978-3-031-40846-5_16

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