The Indian Summer of al-Andalus Mathematics?: An Expanded Addendum (original) (raw)
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As Ahmed Djebbar has pointed out, 11th-century and earlier al-Andalus produced a “solid research tradition in arithmetic”. So far, no continuation of this tradition has been known, but analysis of three sections of two Latin works suggest that they borrow material that can hardly come from elsewhere: 1. The Liber mahameleth, likely to be a more or less free translation made by Gundisalvi or somebody close to him of an Arabic original presenting “mu a¯mala¯t mathematics vom höheren Standpunkt aus” contains systematic variations, for instance of proportions :: p g P G (claimed to deal with prices and goods), where the givens may be sums, differences, products, sums or differences of square roots, etc., solved sometimes by means of algebra, sometimes with appeals to Elements II.5–6, often after reduction by means of proportion techniques. 2. A passage in Chapter 12 of the Liber abbaci first presents the simple version of the recreational problem about the “unknown heritage” (likely to be of late Ancient or Byzantine origin): a father leaves to his first son 1 monetary unit and 1/n of what remains, to the second 2 units and 1/n of what remains, etc.; in the end, all get the same, and nothing remains. Next it goes on with complicated cases where the arithmetical series is not proportional to 1 – 2 – 3 ..., and the fraction is not an aliquot part. Fibonacci gives an algebraic solution to one variant and also general formulae for all variants – but these do not come from his algebra, and he thus cannot have derived them himself. A complete survey of occurrences once again points to al-Andalus. 3. Chapter 15 Section 1 of Fibonacci’s Liber abbaci mainly deals with the ancient theory of means though not telling so. If M is one such mean between A and B, it is shown systematically how each of these three numbers can be found if the other two are given – once more by means of algebra, Elements II.5–6, and proportion techniques. The lettering shows that Fibonacci uses an Arabic or Greek source, but no known Arabic or Greek work contains anything similar. However, the structural affinity suggests inspiration from the same environment as produced the Liber mahameleth. So, this seems to be a non-narrative, a story that was not revealed by the participants, and was not discovered by historians so far.
Contribution to the “9ième Colloque Maghrébin sur l' …, 2007
For some years I have been engaged in a close reading of early Italian abbacus books and related material from the Ibero-Provençal orbit and in comparison of this material with Arabic mathematical writings. At the 7th North African Meeting on the History of Arab Mathematics in Marrakesh in 2002 I presented the first outcome of this investigation: namely that early Italian abbacus algebra was not influenced by the Latin algebraic writings of the 12th-13th centuries (neither by the translations of al-Khwārizmī nor by the works of Fibonacci); instead, it received indirect inspiration from a so far unknown link to the Arabic world, viz to a level of Arabic algebra (probably integrated with mu'āmalāt mathematics) of which very little is known. At the 8th Meeting in Tunis in 2004 I presented a list of linguistic clues which, if applied to Arabic material, might enable us to say more about the links between the Romance abbacus tradition and Arabic mu'āmalāt teaching.
Historia Mathematica 52, p. 26-50, 2020
We present an Arabic treatise on arithmetic, penned in Cherchell (Algeria) around 1575, of which five manuscripts are extant. The author, Ibrāhīm al-Balīshṭār, is a hitherto unknown Morisco mathematician from Aragon. After sketching his biography, we show that his treatise, claimed by him to be the translation of a book by a Christian priest, is actually an elaborate personal work, resulting from the intertwining of two Spanish treatises–those by Marco Aurel and Juan de Ortega–and of material drawn from Arabic authors such as al-Ghurbī, al-ʿUqbānī and Ibn al-Bannāʾ. It is therefore an original attempt to create a Euro-Islamic hybrid knowledge. -------------------------------------- Résumé Nous présentons un traité d'arithmétique en arabe, rédigé à Cherchell (Algérie) vers 1575, dont cinq manuscrits subsistent. L'auteur, Ibrāhīm al-Balīshṭār, est un mathématicien morisque jusqu'ici inconnu, originaire de l'Aragon. Après avoir esquissé sa biographie, nous montrons que son traité, qu'il dit être la traduction d'un livre d'un prêtre chrétien, est en réalité un travail personnel élaboré, résultant de l'entrelacement de deux traités espagnols – ceux de Marco Aurel et Juan de Ortega – et d'éléments tirés d'auteurs arabes comme al-Ghurbī, al-ʿUqbānī et Ibn al-Bannāʾ. Il s'agit donc d'une tentative extraordinaire de création d'un savoir hybride euro-islamique.
India's Contribution to Arab Mathematics (by Khalil Jaouiche)
It is an introductory survey of the influence of India on the mathematics of the Islamic world. some difficulties obviously have cropped up in the study of this subject -namely, paucity of sources, and a focus on astronomy in the existing sources. It is equally hard to disentangle the influence of Greece and China, which may be implicit within the Indian influences. The works of the mathematicians Al-Bi runi -, Al-Khwarizmi -, Al-Karaji and As-Samaw'al are examined in some detail. The Indian contributions especially the work of Brahmagupta and Bhaskara II are explicity highlighted.
Algebra, defined as a method to determine the unknown by means of what is known, given the link between the two, took its initial steps toward disciplinary status during the third/ninth century when al-Khwārizmī produced the first systematic study on the subject. Later Muslim mathematicians followed his lead due to this novel discipline’s propensity for improvement and beneficial application. Thus they applied arithmetic to algebra to make it more practical and open and, as a result, derived great benefits from employing it in matters of inheritance, commerce, land surveys, architecture, and other areas. Roughly 550 years after its formation as a discipline, algebra reached its peak in the aforementioned areas. One of its most famous practitioners, Ibn al-Hā’im, had a lasting and widespread influence first with his commentary on Yāsamīnī and then with his versified work al-Muqni‘ and its commentary al-Mumti‘. However, the latter work eluded the researchers’ attention – perhaps it was overshadowed by the former or lost among the other commentaries – despite its remarkable presentation of the entire conceptual and methodical reper-toire of algebra as it was known at that time, not to mention its analysis of the problems and discussion of the philosophical implications in a long-lasting debate on Islamic mathematical history: Should algebra be arithmetical, geometrical, or both? Which track would be more conducive to improving the discipline so it could break new ground in the historical studies of mathematics? Thus, this article seeks to present the status of Ibn al-Hāim’s al-Mumti‘ fī sharh al-Muqni‘ in the history of mathematics, along with its outstanding features and mathematical analysis. Keywords: mathematics, algebra, Ibn Haim, al-Muqni, al-mumti.
Early Texts on Hindu-Arabic Calculation
Science in Context, 2001
This article describes how the decimal place value system was transmitted from India via the Arabs to the West up to the end of the fifteenth century. The arithmetical work of al-Khwārizmī's, ca. 825, is the oldest Arabic work on Indian arithmetic of which we have detailed knowledge. There is no known Arabic manuscript of this work; our knowledge of it is based on an early reworking of a Latin translation. Until some years ago, only one fragmentary manuscript of this twelfth-century reworking was known (Cambridge, UL, Ii.6.5). Another manuscript that transmits the complete text (New York, Hispanic Society of America, HC 397/726) has made possible a more exact study of al-Khwārizmī's work. This article gives an outline of this manuscript's contents and discusses some characteristics of its presentation.
2019
A Significant Step Toward the Development of Algebra: Al-Samawʾal Ibn Yaḥya Al-Maghribi, a Twelfth Century Mathematician Mustapha Nadmi Mathematics of the Islamic medieval world is still not sufficiently studied. As a result, a goldmine of Islamic medieval books and materials lie unexplored. One manuscript that certainly deserves attention is al-Bāhir fi’l-Jabr (The Shining Treatise on Algebra) of al-Samaw’al ibn Yahya al-Maghribi, a twelfth century mathematician. Al-Bāhir fi’l-Jabr is a manuscript written in Arabic and has never been translated except for a few excerpts in French. The purpose of this study was to explore the mathematical and pedagogical contribution of al-Samaw’al through an analysis of al-Samaw’al’s mathematical techniques and methods in al-Bāhir fi’l-Jabr. Moreover, the treatise provides a precise description of the “arithmetization of algebra”, and gives an accounting of the original ideas of another mathematician, al-Karaji, whose original documents have been l...