Equations and Equating in Arabic Mathematics

Oaks, Jeffrey

doi:10.1484/j.arihs.5.101537

Cited by 8 publications

(10 citation statements)

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“…As an example, here is al-Sulamī's problem (I.6) (I put the corresponding modern symbols in brackets): 6 [Enunciation]…”

Section: Connected Equationsmentioning

confidence: 99%

“…For another example, Euclid's arithmos is radically different from the modern "number", but we should still translate it as "number" and read it with this difference in mind. 8 See [6], Sect. 5.2, for a full discussion.…”

Section: The Structure Of Early Arabic Algebra Booksmentioning

confidence: 99%

“…Then each succeeding one gets three more than the one before, so that the total booty is a hundred twenty-six dirhams." 30 See [9], [6]. 31 [4], p. 151.…”

Section: Problem Typesmentioning

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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“…As an example, here is al-Sulamī's problem (I.6) (I put the corresponding modern symbols in brackets): 6 [Enunciation]…”

Section: Connected Equationsmentioning

confidence: 99%

Section: The Structure Of Early Arabic Algebra Booksmentioning

confidence: 99%

See 1 more Smart Citation

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

Oaks

2015

SHS Web of Conferences

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“…One of several reasons that the algebraic reading is untenable [see Oaks andAlkhateeb 2005, Oaks 2010] is that this māl is named in terms of the algebraic powers in the beginning of the solution, just like the parts of 10. In part 1, Abū Kāmil names the māl 'a thing' ( ) 19 times, which Rashed regards as 'un changement de variable délibéré, purement algébrique,…”

Section: Stage 2 the Equation Is Simplified Using Al-jabr (Restoratimentioning

confidence: 99%

“…Throughout his book, in fact, Rashed sees just about any kind of numerical equating, including arithmetical operations, as an equation. The specific and deliberate mode of stating equations in medieval algebra, which is characterized by both vocabulary and context [see Oaks 2010], becomes lost in Rashed's sea of symbols.…”

Section: Stage 2 the Equation Is Simplified Using Al-jabr (Restoratimentioning

confidence: 99%

Abū Kāmil. Algèbre et analyse Diophantienne. Édition, traduction et commentaire

Rashed¹,

Oaks²

2015

Aest

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After al-Khwārizmī, Abū Kāmil (late ninth century) is the next Arabic author whose book on algebra is extant in its entirety. Where al-Khwārizmī's book was deliberately brief, Abū Kāmil's Kitāb al-jabr wa'l-muqābala (Book of Algebra) occupies 111 folios in the only surviving manuscript. 1 That is long enough for Abū Kāmil to show features and techniques omitted by al-Khwārizmī and to exhibit his own originality with regard to proofs, irrational numbers, and the manipulation of algebraic expressions. Abū Kāmil's influence was deservedly almost as far-reaching as al-Khwārizmī's. The Book of Algebra became a major influence on such well-known figures as al-Karajī, al-Samawʾal, and Ibn al-Bannāʾ, as well as on lesser ones like ʿAlī al-Sulamī and Ibn Badr. Most of the book was translated into Latin in the 12th century and whole portions found their way into the Liber Mahameleth in the 12th century, into Fibonacci's Liber abaci and De practica geometrie in the 13th century, and into Jean de Murs' Liber quadripartitum in the 14th century. From there its influence spread through Italian abbacus texts to Luca Pacioli's Summa de arithmetica of 1494 and into 16th-century European algebra. We also possess several manuscripts of a Hebrew translation made before 1475, possibly in Spain. 2 Two other books of Abū Kāmil are extant. One is his brief Kitāb al-Ṭayr (Book of Birds), in which he uses algebra to solve problems with several ⋆ English translations are mine unless noted otherwise. In referring to Rashed's text,

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Introducing equations in early algebra

Radford

2022

ZDM Mathematics Education

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Equations and Equating in Arabic Mathematics

Cited by 8 publications

References 0 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

Abū Kāmil. Algèbre et analyse Diophantienne. Édition, traduction et commentaire

Introducing equations in early algebra

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