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An Arabic Finger-reckoning Rule Appropriated for Proofs in Algebra - References

Author(s): 
Jeffrey A. Oaks (University of Indianapolis)

References

Abū Kāmil, 2012. Algèbre et Analyse Diophantienne. Edited and translated by Roshdi Rashed. Berlin: De Gruyter. This book gives the Arabic text with a French translation. There is an English translation of the fifteenth century Hebrew translation of this book in [Levey 1966].

Aristotle, n.d. Posterior Analytics, translated by G. R. G. Mure. Available online: http://classics.mit.edu/Aristotle/posterior.html

al-Baghdādī, 1985. Kitāb al-takmila fīʾl-ḥisāb. Edited by A. S. Saidan. Kuwait: Maʿhad al-Makhṭūṭāt al-ʿArabiyaḥ. Contains the Arabic text.

Ibn al-Bannāʾ, 1969. Talkhīṣ aʿmāl al-ḥisāb. Texte établi, annoté et traduit par Mohamed Souissi. Tunis: Université de Tunis. Contains the Arabic text with a French translation.

Ibn al-Bannāʾ, 1994. Rafʿ al-ḥijāb ʿan wujūh aʿmāl al-ḥisāb. Edited by Muḥammad Aballagh. Fās: Jāmiʿat Sīdī Muḥammad ibn ʿAbd Allāh, 1994. Contains the Arabic text.

Ibn al-Hāʾim, 2003. Sharh al-urjūza al-Yāsmīnīya, de Ibn al-Hāʾim. Edited and translated by Mahdi Abdeljaouad. Tunis: Publication de l'Association Tunisienne des Sciences Mathématiques. Contains the Arabic text and a partial French translation.

Ibn al-Yāsamīn, 1993. Muʾallafāt Ibn al-Yāsamīn al-riyāḍiyya [Mathematical Writings of Ibn al-Yāsamīn]. Edited by T. Zemouli. M.Sc. thesis in History of Mathematics, Algiers, E. N. S.

al-Karajī, 1986. al-Kāfī fī l-ḥisāb. Edited by Sami Chalhoub. Aleppo: Aleppo University. Contains the Arabic text.

Levey, Martin (Ed.), 1966. The Algebra of Abū Kāmil: Kitāb fī al-jābr waʾl-muqābala in a Commentary by Mordecai Finzi. Hebrew text, translation and commentary with special reference to the Arabic text. Madison: University of Wisconsin.

Oaks, Jeffrey A., 2009. "Polynomials and equations in Arabic algebra". Archive for History of Exact Sciences 63, 169-203.

Oaks, Jeffrey A., 2010. "Equations and equating in Arabic mathematics". Archives Internationales d'Histoire des Sciences 60, 265-298.

Oaks, Jeffrey A. 2018, "Arithmetical proofs in Arabic algebra". Pp. 215-238 in: Ezzaim Laabid, ed., Actes du 12é Colloque Maghrébin sur l'Histoire des Mathématiques Arabes: Marrakech 26 au 28 mai 2016. Marrakech: École Normale Supérieure. Also available at the author's website: https://www.uindy.edu/cas/mathematics/oaks/files/oaksmarrakech.pdf

Saidan, A. S. 1968, "Finger reckoning in an Arabic poem". The Mathematics Teacher 61, 707-708.

Saidan, A. S, 1971. Tārīkh ʿilm al-ḥisāb al-ʿArabī. ʿAmman: Jamʿiyat ʿUmāl al-Maṭābiʿ al-Taʿāwinīa. Contains the Arabic text of Abūl-Wafāʾ's Kitāb Fīmā yaḥtāju ilayhi al-kuttāb wa-l-ʿummāl wa ghayruhum min ʿilm al-ḥisāb (Book of What is Necessary for Scribes, Dealers, and Others from the Science of Arithmetic).

Saidan, A. S, 1986. Tārīkh ʿilm al-jabr fī l-ʿālam al-ʿArabī. Kuwait: al-Majlis al-Waṭanī lil-Thaqāfah waʿl-Funūn wa-l-Ādāb, Qism al-Turāth al-ʿArabī. Contains the Arabic text of three works on algebra:

  • al-Karajī's al-Fakhrī fī ṣināʿat al-jabr wa-l-muqābala ([Book of] al-Fakhrī on the Art of Algebra),
  • Ibn Badr's Kitāb fīhi ikhtiṣār al-jabr wa-l-muqābala (Brief Book on Algebra), and
  • Ibn al-Bannāʾ's Kitāb al-uṣūl wa-l-muqaddimāt fī l-jabr wa-l-muqābala (Book on the Fundamentals and Preliminaries in Algebra).

Jeffrey A. Oaks (University of Indianapolis), "An Arabic Finger-reckoning Rule Appropriated for Proofs in Algebra - References," Convergence (January 2019)

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