Abstract
On March 2, 1427 [6, p. 32] and [15], Ghiyāth al-Dı̄n Jamshı̄d bin Mas’ūd bin Maḥmood al-Tabı̄b al-Kāshı̄ (or al-Kāshānı̄) completed a monumental book in Arabic on arithmetic called Miftāḥ al-Ḥisāb. The most commonly used translation of this title, the one which we prefer as well, is “Key to Arithmetic.” Other possible translations include “Calculator’s Key” and “Key to Calculation.” Henceforth we will be referring to it as Miftāḥ and its author as al-Kāshı̄. This encyclopedic work includes three general subjects: arithmetic, geometry, and algebra. It comprises five treatises on arithmetic of integers, arithmetic of fractions, arithmetic of sexagesimal numbers, geometry and measurement, and algebra. Al-Kāshı̄ dedicated the Miftāḥ to Ulugh Beg who was the ruler of Samarkand at the time and was a prominent scientist himself. In Berggren’s assessment Miftāḥ was “the crowning achievement of Islamic arithmetic, and truly a gift fit for a king” [12, p. 22]. Saidan agrees by stating “Miftāḥ represents the peak of Islamic arithmetic” [31, p. 29].
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Notes
- 1.
zı̄j is a book of astronomical tables.
References
Aaboe, A.: Al-Kāshı̄’s iteration method for the determination of \(\sin (1^\circ )\). Scr. Math. 20, 24–29 (1954). Reprinted in IMA56, pp. 354–360
Al-Kāshı̄: Miftāḥ al-Ḥisab. Manuscript Nuruosmaniye 2967, Istanbul, Turkey
Al-Kāshı̄: Miftāḥ al-Ḥisab. Edition, and translation by Ahmad Sa’id al-Dimirdash and Muhammad amdi al-Hifni al-Shaykh. Dar al-Katib al-Arabi, Cairo (1969)
Al-Kāshı̄: Miftāḥ al-Ḥisab. Edition, notes and translation by Nabulsi Nader. University of Damascus Press, Damascus (1977)
Aydin, N., Hammoudi, L.: Root extraction by Al-Kāshı̄ and Stevin. Arch. Hist. Exact Sci. 69(3), 291–310 (2015)
Azarian, M.K.: A summary of the mathematical works of Giyath ud-din Jamshı̄d Kāshāni. J. Recreat. Math. 29(1), 32–42 (1998)
Bagheri, M.: A newly found letter of Al-Kāshı̄ on scientific life in Samarkand. Hist. Math. 24, 241–256 (1997)
Bartold, V.V.: Ulugbek and his time Petrograd. Printing House of the Russian Academy of Sciences, 188 p. (In Russian) (1918)
Berggren, J.L.: Episodes in the Mathematics of Medieval Islam, 2nd edn. Springer, Berlin (2016)
Dold-Samplonius, Y.: Practical Arabic mathematics: measuring the muqarnas by al-Kāshı̄. Centaurus 35(34), 193–242 (1992)
Dold-Samplonius, Y.: Al-Kāshı̄, in Encyclopedia Britannica. https://www.britannica.com/biography/al-Kashi. Accessed 5 July 2018
Hogendijk, J.P.: Al-Kāshı̄’s determination of π to 16 decimals in an old manuscript. Zeitschrift für Geschichte der arabisch-islamischen Wissenschaften 18, 73–152 (2009)
Hogendijk, J.P.: Sources relating to Ghiyāth Al-Din Kāshāni, or Al-Kāshı̄. http://www.jphogendijk.nl/arabsci/kashi.html. Accessed July 2017
İzgi, C.: Osmanlı Medreselerinde İlim (Sciences in the Ottoman Schools). İz Yayıncılık, Topkapı(1997)
Kennedy, E.S.: The Planetary Equatorium of Jamshı̄d Ghiyāth al-Din al-Kāshı̄. Princeton University Press, New Jersey (1960)
Kennedy, E.S.: A letter of Jamshı̄d al-Kāshı̄ to his father: scientific research and personalities at a fifteenth century court. Orientalia 29, 191–213 (1960). Reprinted in Edward S. Kennedy, colleagues and former students, Studies in the Islamic Exact Sciences, pp. 722–744. American University, Beirut (1983)
O’Conner, J.J., Robertson, E.F.: The MacTutor History of Mathematics Archive. http://www-history.mcs.st-and.ac.uk/Biographies/Al-Kashi.html. Reterived July 2017
Qurbani, A.: Kāshāni Nameh, Publication No. 1322 of Tehran University, Tehran, Iran, 1350 A.H.S. (1971)
Riahi, F.: An early iterative method for determination of \(\sin (1^\circ )\). Coll. Math. J. 26(1), 16–21 (1995)
Rosenfeld, B.A., İhsanoğlu, E.: Mathematicians, Astronomers, and Other Scholars of Islamic Civilization and Their Works (7th-19th C.). Research Centre for Islamic History Art and Culture (IRCICA), Istanbul (2003)
Rosenfeld, B.A., Segal, V.S., Youschkevitch, A.P.: Klyuch Arifmetiki (Key to Arithmetic). Traktat ob Okruzhnosti, Moscow (1956)
Saidan, A.: The Arithmetic of al-Uqlı̄disı̄: The Story of Hindu-Arabic Arithmetic as Told inKitāb al-fuṣūl fı̄ al-Ḥisāb al-Hindı̄. Translated and Annotated by A.S. Saidan. Reidel Publishing, Dordrecht (1978)
Saliba, G.: Islamic Science and the Making of the European Renaissance. The MIT Press, Cambridge (2007)
Sayılı, A.: The Observatory in Islam and Its Place in the General History of Observatory. Turkish Historical Society Publication, Ankara (1960)
Sayılı, A.: Uluğ Bey ve Semerkanddeki İlim Faaliyeti Hakkında Giyasuddini Kaşi’nin Mektubu: Ghiyāth al-Din al-Kāshı̄’s Letter on Ulugh Beg and the Scientific Activity in Samarqand. Turk Tarih Kurumu Basimevi, Ankara (1960)
Sezgin, F.: İslamda Bilim ve Teknik, Volume I (Science and Technology is Islam). Translation to Turkish from German by A. Aliy. Turkish Academy of Sciences Publication, Ankara (2007)
Suter, H.: Die Mathematiker und Astronomen und ihre Werke. Abhandl. zur Geschichte der mathematischen Wissenschaften, Heft 10, 173–174 (1900)
Taani, O.H.: An analysis of the contents and pedagogy of al-Kāshı̄’s 1427 “Key to Arithmetic” (Miftāḥ Al-Ḥisab). Ph.D. dissertation, New Mexico State University, New Mexico State University, ProQuest Dissertations Publishing, 3534149 (2011)
Taani, O.: Multiple paths to mathematics practice in al-Kāshı̄s key to arithmetic. Sci. Educ. 23(1), 125–141 (2014)
Youschkevitch, A.P., Rosenfeld, B.A.: Al-Kāshı̄, in Dictionary of Scientific Biography, vol. 7, pp. 255–262. Charles Scribner’s Sons, New York (1973)
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Aydin, N., Hammoudi, L. (2019). Introduction. In: Al-Kāshī's Miftāḥ al-Ḥisab, Volume I: Arithmetic. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-14950-5_1
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