Māl, enunciations, and the prehistory of Arabic algebra

Oaks, Jeffrey; Alkhateeb, Haitham M.

doi:10.1016/j.hm.2005.03.002

Cited by 20 publications

(15 citation statements)

References 15 publications

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“…5.2, for a full discussion. 9 Page numbers are from Rashed's edition [4,5]. 10 Problem (7) in the Oxford manuscript was probably added later, so Rashed's edition shows 34 problems.…”

Section: The Structure Of Early Arabic Algebra Booksmentioning

confidence: 99%

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

Oaks

2015

SHS Web of Conferences

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Abstract. In his introductory book on algebra Alī al-Sulamī (10th c.) pays careful attention to the arrangement of his 78 worked-out problems, balancing his borrowings with his overall structure. His collection is put into context by comparing it with the problems in the books of three other early Arabic algebraists. It is shown that unlike al-Khwārizmī and Abū Kāmil, al-Sulamī orders his problems carefully. He gives a global ordering based on equation type that is an inversion of the local ordering of his predecessors, and he exhibits a local ordering that is a consequence of his appropriation of diverse problem types within his collection.

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“…5.2, for a full discussion. 9 Page numbers are from Rashed's edition [4,5]. 10 Problem (7) in the Oxford manuscript was probably added later, so Rashed's edition shows 34 problems.…”

Section: The Structure Of Early Arabic Algebra Booksmentioning

confidence: 99%

“…15 Here the word māl takes its algebraic meaning. 16 See [8,9] for a description of this method. 17 Page numbers are from [1] and [2].…”

Section: -P4mentioning

confidence: 99%

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

Oaks

2015

SHS Web of Conferences

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“…Some have done so with the aim of establishing the correct meaning with the aid of Arabic etymology and linguistics (e.g. Gandz 1926, Saliba 1972, Oaks and Alkhateeb 2005. Strictly taken, the precise meaning of these Arabic terms and concepts is irrelevant for our study.…”

Section: Starting Pointmentioning

confidence: 99%

“…In the yet to be published Høyrup (2006) and Oaks and Alkhateeb (2005) the double meaning of the māl is prominently present in their interpretation of early Arabic algebra. Høyrup (2006) adequately describes the anomaly as "the square root of real money".…”

Section: The Ambiguity Of Mālmentioning

confidence: 99%

A Conceptual Analysis of Early Arabic Algebra

Heeffer

2008

The Unity of Science in the Arabic Tradition

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Arabic algebra derives its epistemic value not from proofs but from correctly performing calculations using coequal polynomials. This idea of 'mathematics as calculation' had an important influence on the epistemological status of European mathematics until the seventeenth century. We analyze the basic concepts of early Arabic algebra such as the unknown and the equation and their subsequent changes within the Italian abacus tradition. We demonstrate that the use of these concepts has been problematic in several aspects. Early Arabic algebra reveals anomalies which can be attributed to the diversity of influences in which the al-jabr practice flourished. We argue that the concept of a symbolic equation as it emerges in algebra textbooks around 1550 is fundamentally different from the 'equation' as known in Arabic algebra.

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The Miftāḥ Translation

Aydın

Hammoudi

2019

Al-Kāshī's Miftāḥ Al-Ḥisab, Volume I: Arithmetic

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Māl, enunciations, and the prehistory of Arabic algebra

Cited by 20 publications

References 15 publications

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

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

A Conceptual Analysis of Early Arabic Algebra

The Miftāḥ Translation

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