Variables, limits, and infinitesimals in Portugal in the late 18th century

Domingues, João Caramalho

doi:10.1016/s0315-0860(03)00004-1

Cited by 3 publications

(1 citation statement)

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“…For instance, the function concept depends on the variable concept and today's variable concept differs significantly from the variable concept that Euler had at his disposal. Domingues (2004) points out that most mathematicians during the 18th century regarded variables as being quantities that vary, that change in magnitude. For instance, the mathematician Guillaume de l 'Hospital (1661'Hospital ( -1704 defined variables in the follonging way: 6 "We call variable quantities those that increase or decrease continuously; and to the contrary we call constant quantities those that remain the same while the others change" (l 'Hospital, 1696, p. 1).…”

Section: The Problem Of Not Considering Different Conceptual Frameworkmentioning

confidence: 99%

On the relations between historical epistemology and students’ conceptual developments in mathematics

Bråting

Pejlare

2015

Educ Stud Math

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There is an ongoing discussion within the research field of mathematics education regarding the utilization of the history of mathematics within mathematics education. In this paper we consider problems that may emerge when the historical epistemology of mathematics is paralleled to students' conceptual developments in mathematics. We problematize this attempt to link the two fields on the basis of Grattan-Guinness' distinction between "history" and "heritage". We argue that when parallelism claims are made, history and heritage are often mixed up, which is problematic since historical mathematical definitions must be interpreted in its proper historical context and conceptual framework. Furthermore, we argue that cultural and local ideas vary at different time periods, influencing conceptual developments in different directions regardless of whether historical or individual developments are considered, and thus it may be problematic to uncritically assume a platonic perspective. Also, we have to take into consideration that an average student of today and great mathematicians of the past are at different cognitive levels.

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Section: The Problem Of Not Considering Different Conceptual Frameworkmentioning

confidence: 99%

On the relations between historical epistemology and students’ conceptual developments in mathematics

Bråting

Pejlare

2015

Educ Stud Math

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Why Historical Research Needs Mathematicians Now More Than Ever

Blåsjö

2023

Archimedes

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Geometry and analysis in Anastácio da Cunha’s calculus

Domingues¹

2023

Arch. Hist. Exact Sci.

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It is well known that over the eighteenth century the calculus moved away from its geometric origins; Euler, and later Lagrange, aspired to transform it into a “purely analytical” discipline. In the 1780 s, the Portuguese mathematician José Anastácio da Cunha developed an original version of the calculus whose interpretation in view of that process presents challenges. Cunha was a strong admirer of Newton (who famously favoured geometry over algebra) and criticized Euler’s faith in analysis. However, the fundamental propositions of his calculus follow the analytical trend. This appears to have been possible due to a nominalistic conception of variable that allowed him to deal with expressions as names, rather than abstract quantities. Still, Cunha tried to keep the definition of fluxion directly applicable to geometrical magnitudes. According to a friend of Cunha’s, his calculus had an algebraic (analytical) branch and a geometrical branch, and it was because of this that his definition of fluxion appeared too complex to some contemporaries.

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Variables, limits, and infinitesimals in Portugal in the late 18th century

Cited by 3 publications

References 10 publications

On the relations between historical epistemology and students’ conceptual developments in mathematics

On the relations between historical epistemology and students’ conceptual developments in mathematics

Why Historical Research Needs Mathematicians Now More Than Ever

Geometry and analysis in Anastácio da Cunha’s calculus

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