Series of problems in Arabic algebra: The example of ʿAlī al-Sulamī

Oaks, Jeffrey

doi:10.1051/shsconf/20152200005

Cited by 2 publications

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References 2 publications

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“…Tannery 1893; for al-Sulamī's Sufficient Introduction on Calculation by Algebra and What One Can Learn from its Examples, problem 49, cf. Oaks (2015); for al-Khwārizmī's Algebra, problem <1>, cf. Rashed 2009, 156-8 (adapted): we replaced the modern terms "plus" and "minus," applied by Rashed, with "and" and "less," respectively.…”

Section: Diophantus Al-sulamī Al-khwārizmīmentioning

confidence: 99%

Situating the Debate on “Geometrical Algebra” within the Framework of Premodern Algebra

Sialaros¹,

Christianidis²

2016

Sci Context

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Argument The aim of this paper is to employ the newly contextualized historiographical category of "premodern algebra" in order to revisit the arguably most controversial topic of the last decades in the field of Greek mathematics, namely the debate on "geometrical algebra." Within this framework, we shift focus from the discrepancy among the views expressed in the debate to some of the historiographical assumptions and methodological approaches that the opposing sides shared. Moreover, by using a series of propositions related to Elem. II.5 as a case study, we discuss Euclid's geometrical proofs, the so-called "semi-algebraic" alternative demonstrations attributed to Heron of Alexandria, as well as the solutions given by Diophantus, al-Sulamī, and al-Khwārizmī to the corresponding numerical problem. This comparative analysis offers a new reading of Heron's practice, highlights the significance of contextualizing "premodern algebra," and indicates that the origins of algebraic reasoning should be sought in the problem-solving practice, rather than in the theorem-proving tradition.

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Section: Diophantus Al-sulamī Al-khwārizmīmentioning

confidence: 99%

Situating the Debate on “Geometrical Algebra” within the Framework of Premodern Algebra

Sialaros¹,

Christianidis²

2016

Sci Context

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Les séries de problèmes, un genre au carrefour des cultures : une première synthèse

Bernard

2015

SHS Web of Conferences

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Résumé. Cet article propose une présentation du volume « les séries de problèmes, un genre au carrefour des cultures » et une vue d'ensemble des principales questions qui y sont abordées. La première partie décrit le contexte du projet qui y a donné naissance au sein du labex HASTEC, ainsi que l'objectif du volume et les conditions dans lesquelles il a été préparé. La seconde partie décrit le coeur du projet scientifique. On présente d'abord (2.1) une définition de son thème directeur, les problèmes qu'elle pose et les différentes manières dont il a été compris par les contributeurs ou contributrices. On résume ensuite (2.2) quatre grandes directions d'interprétation possibles des « séries de problèmes » en termes d'histoire culturelle : en lien à des visées encyclopédiques ; en lien à des fins pédagogiques ; comme objet de transformation et de réappropriation permanente ; comme support de légitimité savante.Abstract. Series of problems, a genre at the crossroads of cultures: a first synthesis. This paper presents the volume entitled "series of problems, a genre at the crossroad of cultures" and offers a general view of the main questions that are addressed in it. The first part describes the institutional context of the project that gave rise to it within labex HASTEC, as well as the objective of this volume and the conditions in which it was prepared. The second part describes the core of the scientific project. It first presents (2.1) a definition of its leading subject, the problems this definition raises and the various ways in which it has been understood by the contributors. It then summarizes (2.2) four main directions of possible interpretation of "series of problems" in terms of cultural history: in relation to encyclopedic intentions; in relation to didactic ends; as an object of permanent transformation and re-appropriation; as support of scientific legitimacy. Préambule

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Series of problems in Arabic algebra: The example of ʿAlī al-Sulamī

Cited by 2 publications

References 2 publications

Situating the Debate on “Geometrical Algebra” within the Framework of Premodern Algebra

Situating the Debate on “Geometrical Algebra” within the Framework of Premodern Algebra

Les séries de problèmes, un genre au carrefour des cultures : une première synthèse

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