32 research outputs found
Al-Hawārī’s commentary on Ibn al-Bannā’’s Talkhīs: Contents and influences
In 1305 al-Hawārī completed his commentary on Ibn al-Bannā’’s famous arithmetic book Talkhī½ṣ aþmāl al-¬isāb . This is the only commentary, apart from Ibn al-Bannā’’s own, to have been written during the author’s lifetime. What distinguishes al-Hawārī’s book from the numerous later commentaries is its focus on numerical examples of the rules of calculation. We present here what we know about the author, his book, its salient features, and its influences
Series of problems in Arabic algebra: The example of ʿAlī al-Sulamī
In his introductory book on algebra ʿAlī 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
Jacques Sesiano, An Ancient Greek Treatise on Magic Squares
The two earliest Arabic treatises explaining the construction of magic squares date from the 10th century ad. One is found in the Commentary on the Arithmetical [Introduction] (Kitāb tafsīr al-Arithmāṭīqī) by ʿAlī ibn Aḥmad al-Anṭākī (d. 376 H/ad 987). Only book 3 of the original three books is extant, and that in a single manuscript. This book is divided into three chapters: the first is a collection of arithmetical definitions, statements of propositions, and identities assembled from Greek and Arabic sources; the second is on magic squares; and the third deals with “hidden numbers”, in which a person thinks of a number and another discovers it after operations are performed on it. Curiously, none of these chapters have anything to do with Nicomachus’ Arithmetical Introduction, on which the book is supposed to be a commentary.
Reviewed by: Jeffrey A. Oaks
Published Online (2022-07-31)Copyright © 2022 by Jeffrey A. Oaks
Article PDF Link: https://jps.library.utoronto.ca/index.php/aestimatio/article/view/39089/29778
Corresponding Author: Jeffrey A. Oaks,University of IndianapolisE-Mail: [email protected]
Abū Kāmil. Algèbre et analyse diophantienne. Édition, traduction et commentaire by Roshdi Rashed
Practicing algebra in late antiquity: The problem-solving of Diophantus of Alexandria
Medieval algebra is distinguished from other arithmetical
problem-solving techniques by its structure and technical vocabulary. In
an algebraic solution one or several unknowns are named, and via
operations on the unknowns the problem is transferred to the artificial
setting of an equation expressed in terms of the named powers, which is
then simplified and solved. In this article we examine Diophantus’
Arithmetica from this perspective. We find that indeed Diophantus’
method matches medieval algebra in both vocabulary and structure. Just
as we see in medieval Arabic and Italian algebra, Diophantus worked out
the operations expressed in the enunciation of a problem prior to
setting up a polynomial equation. Further, his polynomials were regarded
as aggregations with no operations present. (c) 2012 Elsevier Inc. All
rights reserved