Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-06T13:51:34.025Z Has data issue: false hasContentIssue false
  • English
  • Français

History of Mathematics in the Islamic World: The Present State of the Art

Published online by Cambridge University Press:  09 March 2016

J. L. Berggren
J. L. Berggren*
Affiliation:
Simon Fraser University
Get access Rights & Permissions [Opens in a new window]

Extract

In Recent Years, many discoveries in the history of Islamic mathematics have not been reported outside the specialist literature, even though they raise issues of interest to a larger audience. Thus, our aim in writing this survey is to provide to scholars of Islamic culture an account of the major themes and discoveries of the last decade of research on the history of mathematics in the Islamic world. However, the subject of mathematics comprised much more than what a modern mathematician might think of as belonging to mathematics, so our survey is an overview of what may best be called the “mathematical sciences” in Islam; that is, in addition to such topics as arithmetic, algebra, and geometry we will also be interested in mechanics, optics, and mathematical instruments.

Type
Research Article
Information
Review of Middle East Studies , Volume 19 , Issue 1 , July 1985 , pp. 9 - 33
Copyright
Copyright © Middle East Studies Association of North America 1985

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Ahmad, Salah, and Rashed, Roshdi 1972. Eds. Al-Bāhir en algèbre d’as-Samaw’al. In French and Arabic. Damascus: University Press of Damascus.Google Scholar
Ali, Jami 1967. Trans. The determination of the coordinates of cities. Beirut: American University of Beirut Press.Google Scholar
Anbouba, Adel 1977. See Anbouba, 1978b.Google Scholar
Anbouba, Adel 1978a. L’algèbre arabe aux IXe et Xe siècles. Aperçu général. Journal for the History of Arabie Science 2:66–100.Google Scholar
Anbouba, Adel 1978b. Construction de l’heptagone régulier par les Arabes au 4e siècle de l’hégire. Journal for the History of Arabie Science 2:264–69. This is a summary of the much more extensive Arabic article that appeared in the same journal, vol. 1 (1977): 352–84.Google Scholar
Anbouba, Adel 1979. Un traité d’Abū Ja’far (al-Khāzin) sur les triangles rectangles numériques. Journal for the History of Arabic Science 3:134–78.Google Scholar
Anbouba, Adel 1982. Un mémoire d’al-Qaīṣī (4e siècle H.) sur certaines sommations numériques. Journal for the History of Arabic Science 6(1–2):208–81.Google Scholar
Berggren, J. L. 1980. A comparison of four analemmas for determining the azimuth of the Qibla. Journal for the History of Arabic Science 4:69–80.Google Scholar
Berggren, J. L. 1981a. On al-Biruni’s ‘Method of the Zijes’ for the Qibla. In Proceedings of the 16th International Congress of the History of Science, Section C, 237–45. Bucharest: Academy of the Socialist Republic of Romania.Google Scholar
Berggren, J. L. 1981b. An anonymous treatise on the regular nonagon. Journal for the History of Arabic Science 5:37–41.Google Scholar
Berggren, J. L. 1982. Al-Bīrūnī on plane maps of the sphere. Journal for the History of Arabic Science 6:47–112.Google Scholar
Berggren, J. L. 1984(?). On the origins of al-Bīrūnī’s ‘Method of the Zījes’ in the theory of sundials. To appear in Centauras.Google Scholar
Berggren, J. L. 1985. Spherical trigonometry in the zīj of Kūshyār ibn Labbān. To appear in King and Saliba 1985.Google Scholar
Bulgakov, P. G. 1962. Ed. Taḥdīd nihāyāt al-amākin li-taṣḥīḥ masāfāt al-masākin. Published in “Majallat ma’had al-makhṭūṭāt al-’arabiyya.” Cairo: The Arab League.Google Scholar
Busard, H. L. L., and Konigsveld, P. S. van 1973. Der Liber de arcibus similibus des Ahmed ibn Jusuf. Annals of Science 30(4):381–406.Google Scholar
Debarnot, M.-Th. 1978. Introduction du triangle polaire par Abū Naṣr b. ‘Irāq. Journal for the History of Arabic Science 2(1):126–36.Google Scholar
Debarnot, M.-Th. 1980. Les Clefs d’astronomie d’Abū al-Rayḥān… al-Bīrūnī: La trigonometrie sphérique chez les arabes de l’est à la fin du Xe siècle. Thèse du 3eme cycle. Paris.Google Scholar
Djebbar, Ahmad 1981. Enseignement et recherche mathématiques dans le Maghreb des XIIIe-XIVe siècles. Publications mathématiques d’Orsay. Paris: Université de Paris-Sud.Google Scholar
Djebbar, Ahmad 1985. L’analyse combinatoire au Maghreb: l‘example d’ibn Mun‘im (XIIe-XIIIe siècles). Publications mathématiques d’Orsay. Paris: Université de Paris-Sud.Google Scholar
Ehrenkreutz, Andrew S. 1962. The kurr system in medieval Iraq. Journal Econ. Soc. Hist, of Orient 5:309–314.Google Scholar
Ehrenkreutz, Andrew S. 1964. The taṣrīf and Tas‘īr calculations in medieval Mesopotamian fiscal operations. Journal Econ. Soc. Hist, of Orient 7:46–56.Google Scholar
Engroff, J. W. 1980. The Arabic tradition of Euclid’s elements. Book V. Ph.D. dissertation, Harvard University.Google Scholar
Gandz, Solomon 1938. The algebra of inheritance. Osiris 5:319–91.Google Scholar
Hamadanizadeh, Javad 1976. Medieval interpolation theory. Ph.D. Dissertation, Teacher’s College, Columbia University.Google Scholar
Hamadanizadeh, Javad 1978. Interpolation schemes in Dastūr al-Munajjimīn. Centauras 2(2):44–52.Google Scholar
Hamadanizadeh, Javad 1980. The trigonometric tables of al-Kāshī in his Zīj-i khāqānī. Historia Mathematica 7:38–45.CrossRefGoogle Scholar
Hartner, W. 1965. Al-Djabr wa’l-muḳābala. In Encyclopedia of Islam, ed. 2, vol. 2, 360–62. Leiden: E. J. Brill.Google Scholar
Hermelink, Heinrich 1975. The earliest reckoning books existing in the Persian language. Historia Mathematica 2:299–303.Google Scholar
Hermelink, Heinrich 1978. Arabische Unterhaltungsmathematik als Spiegel jahrtausendealter Kulturbeziehungen zwischen Ost und West. Janus 65:105–17.Google Scholar
Hocheim, A. 1877–80. Trans. Al-Kāfī fīl ḥisāb. 3 pts. Halle/Saale.Google Scholar
Hogendijk, Jan P. 1981. How trisections of the angle were transmitted from Greek to Islamic geometry. Historia Mathematica 8:417–38.Google Scholar
Hogendijk, Jan P. 1984a. Ibn al-Haytham’s completion of the Conics. Heidelberg: Springer Verlag.Google Scholar
Hogendijk, Jan P. 1984b. Greek and Arabic constructions of the regular heptagon. Archive for History of Exact Sciences 30:197–330.Google Scholar
Hogendijk, Jan P. 1985. Thābit ibn Qurra knew the pair of amicable numbers 17296, 18146. To appear in Historia Mathematica.Google Scholar
Irani, R. A. K. 1956. The Jadwal al-taqwīm of Ḥabash al-Ḥāsib. Unpublished master’s dissertation, American University of Beirut.Google Scholar
Jaouiche, Khalil 1976. Ed. and trans. Le livre du qarasṭūn de Ṯābit ibn Qurra. Leiden: E. J. Brill.Google Scholar
Jensen, Claus 1971. Abū Naṣr Manṣūr’s approach to spherical astronomy as developed in his treatise “The table of minutes.” Centaurus 16(1):1–19.Google Scholar
Kennedy, Edward S. 1968. The exact sciences in Iran under the Saljuqs and Mongols. In Cambridge History of Iran, 5:659–79. Cambridge: Cambridge University Press.Google Scholar
Kennedy, Edward S. 1969. An overview of the history of trigonometry. In Historical Topics for the Mathematics Classroom, 333–59. Washington, D.C.: National Council of Teachers of Mathematics. Reprinted in Kennedy et al. 1983.Google Scholar
Kennedy, Edward S. 1970. The Arabic heritage in the exact sciences. Al-Abhath 23:327–44. Reprinted in Kennedy et al. 1983.Google Scholar
Kennedy, Edward S. 1973. A commentary upon Biruni’s Kitāb taḥdīd al-amākin. Beirut: University of Beirut Press.Google Scholar
Kennedy, Edward S. 1976. The exhaustive treatise on shadows by Abū al-Rayḥān al-Bīrūnī. Vol. 1, trans., vol. 2, commentary. Aleppo: Institute for History of Arabic Science.Google Scholar
Kennedy, Edward S. 1984. Applied mathematics in the tenth century: Abu’l-Wafā’ calculates the distance Baghdad-Mecca. Historia Mathematica 11:193–206.Google Scholar
Kennedy, Edward S., et al. 1983. Studies in the Islamic exact sciences. Beirut: American University of Beirut Press.Google Scholar
Kennedy, Edward S., and Debarnot, M.-Th. 1984(?). Two mappings proposed by Bīrūnī, . To appear in Zeitschrift fur Geschichte der arabisch-Islamischen Wissenschaften.Google Scholar
King, David A. 1972. The astronomical works of Ibn Yūnus. Ph.D. dissertation, Yale University.Google Scholar
King, David A. 1973. Al-Khalīlī’s auxiliary tables for solving problems of spherical astronomy. Journal for the History of Astronomy 4:99–110.Google Scholar
King, David A. 1974a. On medieval multiplication tables. Historia Mathematica 1:317–23. Reprinted in King 1985a.Google Scholar
King, David A. 1974b. An analog computer for solving problems of spherical astronomy. Archive internat, d’hist. des sciences 24:219–42. Reprinted in King 1986.Google Scholar
King, David A. 1979a. Notes on the sources for the history of early Islamic mathematics. Journal of the American Oriental Society 99:450–59.Google Scholar
King, David A. 1979b. Ḳibla. In Encyclopedia of Islam, ed. 2, vol. 5:83–88. Leiden: E. J. Brill.Google Scholar
King, David A. 1979c. Supplementary notes on medieval Islamic multiplication tables. Historia Mathematica 6:405–17. Reprinted in King 1985a.Google Scholar
King, David A. 1980. The exact sciences in medieval Islam: Some remarks on the present state of research. Middle East Studies Association Bulletin 14(1):10–26.Google Scholar
King, David A. 1981, 1985(?). A catalog of the scientific manuscripts in the Egyptian National Library. 2 vols. Cairo: American Research Center in Egypt.Google Scholar
King, David A. 1981. Universal solutions in medieval Islamic astronomy. Abstract of talk, in Proceedings of the 16th Internat. Congress of the History of SciencePart A., 144. Bucharest: Acad, of the Socialist Republic of Romania.Google Scholar
King, David A. 1983a. The astronomy of the Mamluks. Isis 74:531–55. Reprinted in King 1985a.Google Scholar
King, David A. 1983b. Al-Khwārizmī and new trends in mathematical astronomy in the ninth century. New York: Hagop Kevorkian Center for Near Eastern Studies, NYU.Google Scholar
King, David A. 1984. A survey of the scientific manuscripts in the Egyptian National Library. Malibu, Calif.: Undena Publ.Google Scholar
King, David A. 1985a. Islamic mathematical astronomy. London: Variorum Reprints.Google Scholar
King, David A. 1985b. Some early Islamic approximate methods for determining the Qibla. To appear in King and Saliba 1985.Google Scholar
King, David A. 1986. Islamic astronomical instruments. London: Variorum Reprints.Google Scholar
King, David A., and Saliba, George A. 1985. Eds. Festschrift: A volume of studies of the history of science in the Near East, dedicated to E. S. Kennedy. New York: New York Academy of Sciences. In press.Google Scholar
Knorr, Wilbur 1983. On the transmission of geometry from Greek into Arabic. Historia Mathematica 10:71–78.Google Scholar
Lorch, Richard 1984. Qibla diagrams and associated instruments. To appear.Google Scholar
Lorch, Richard 1985. Al-Ṣaghānī’s treatise on projecting the sphere. To appear in King and Saliba 1985.Google Scholar
Luckey, P. 1951. Die Rechenkunst bei Ğamsīd b. Mas’ūd al-Kāshī. Abhandlungen fur die Kunde des Morgenlandes (Wiesbaden: Deutsche Morgenlandische Gesellschaft) 31.Google Scholar
Mach, Rudolf. 1977. Catalogue of Arabic manuscripts (Yahuda Collection) in the Garrett Collection, Princeton University. Indexed by McChesney, R. D.. Princeton: Princeton University Press.Google Scholar
Matvievskaya, Galina 1985. The theory of quadratic irrationals in medieval oriental mathematics. To appear in King and Saliba 1985.Google Scholar
Muwafi, Amin, and Philippou, A. N. 1981. An Arabic version of Eratosthenes on mean proportionals. Journal for the History of Arabic Science 5:147–74.Google Scholar
Naini, Alireza Djafari 1982. Geschichte der Zahlentheorie im Orient. Braunschweig: Verlag Klose and Co.Google Scholar
Plooij, Edward B. 1950. Euclid’s conception of ratio… as criticized by Arabian commentators. Doctoral dissertation, Rijksuniversiteit te Leiden.Google Scholar
Rashed, Roshi 1972. L’induction mathématique: al-Karajī, as-Samaw’al. Archive for History of Exact Sciences 9:1–21.Google Scholar
Rashed, Roshi 1973. Algèbre et linguistique: l’analyse combinatoire dans la science arabe. In Boston Studies in the Philosophy of Sciences, ed. Cohen, R., 383–99. Dordrecht: D. Reidel.Google Scholar
Rashed, Roshi 1974. Résolution des equations numériques et algèbre: Šaraf-al-Dīn al-Ṭūsī, Viète. Archive for the History of Exact Sciences 12:244–90.Google Scholar
Rashed, Roshi 1975a. Ed. L’art de l’algèbre de Diophante. Cairo: Maṭabi’ al-hai’a al-miṣriyya al-’āmma al-kitāb.Google Scholar
Rashed, Roshi 1975b. Récommencements de l’algèbre au XIe et XIIe siècles. In The Cultural Context of Medieval Learning, ed. Murdoch, John E. and Sylla, Edith D., 33–60. Dordrecht: D. Reidel.Google Scholar
Rashed, Roshi 1978. L’extraction de la racine nième et l’invention des fractions decimales (XIe-XIIe siècles). Archive for History of Exact Sciences 18:191–243. Reprinted in Rashed 1984a.Google Scholar
Rashed, Roshi 1979a. L’analyse diophantienne au Xe siècle: l’example d’al-Khāzin. Rev. Histoire Sci. Appl. 32(3):193–222. Reprinted in Rashed 1984a.Google Scholar
Rashed, Roshi 1979b. La construction de l’heptagone régulier par Ibn al-Haytham. Journal for the History of Arabic Science 3(2):309–87.Google Scholar
Rashed, Roshi 1980. Ibn al-Haytham et le théorème de Wilson. Archive for History of Exact Sciences 22(4):305–21. Reprinted in Rashed 1984a.Google Scholar
Rashed, Roshi 1983. Nombres amiables, parties aliquotes et nombres figurés au XIIIeme-XIVeme siècles. Archive for History of Exact Sciences 28(2):107–47. Reprinted in Rashed 1984a.Google Scholar
Rashed, Roshi 1984a. Entre arithmétique et algèbre: recherches sur l’histoire des mathématiques arabes. Paris: Les Belles Lettres.Google Scholar
Rashed, Roshi 1984b. Ed. and trans. Diophante: les arithmétiques. Tome III (livre IV), tome IV (livres V, VI, VII). Paris: Les Belles Lettres.Google Scholar
Rashed, Roshdi, and Djebbar, Ahmad 1981. L’Œuvre algébrique d’al-Khayyām. Aleppo: Institute for the History of Arabic Science.Google Scholar
Richter-Bernburg, Lutz 1982. Al-Bīrūnī’s Maqāla fī tasṭīḥ al-ṣuwar wa-tabṭīkh al-kuwar. Journal for the History of Arabic Science 6:113–22.Google Scholar
Rosenfeld, Boris A. 1978. Review of Fuat Sezgin’s Geschiehte des arabischen Schrifttums, Bd. 5. Archives Internat. Hist. Sciences 28:325–29.Google Scholar
Rozhanskaya, Miriam 1985. On a mathematical problem in al-Khāzinī’s Book of the Balance of Wisdom. To appear in King and Saliba 1985.Google Scholar
Rozhanskaya, Miriam, and Rosenfeld, Boris A. 1985. On al-Bīrūnī’s Densimetry. To appear in King and Saliba 1985.Google Scholar
Sabra, A. I. 1968. Thābit ibn Qurra on Euclid’s parallels postulate. Journal of the Warburg and Courtauld Institutes 31:12–32.Google Scholar
Sabra, A. I. 1969. Simplicius’s proof of Euclid’s parallels postulate. Journal of the Warburg and Courtauld Institutes 32:1–24.CrossRefGoogle Scholar
Sabra, A. I. 1971. Ilm al-ḥisāb. In Encyclopedia of Islam, ed. 2, vol. 3:1138–41.Google Scholar
Sabra, A. I. 1982. Ibn al-Haytham’s lemmas for solving ‘Alhazen’s problem.’ Archive for History of Exact Sciences 26:299–324.Google Scholar
Sabra, A. I. 1983. Ed. Kitāb al-manāẓir (The Optics of Ibn al-Haytham). Arabic text of books 1, 2, and 3 on direct vision. Kuwait: National Council for Culture, Arts, and Letters, Arabic Heritage Dept.Google Scholar
Saidan, Ahmad S. 1966. The earliest extant Arabic arithmetic. Isis 57:475–90. See also Saidan, 1978a.Google Scholar
Saidan, Ahmad S. 1971. Ilm al-ḥisāb al-’Arabī: ḥisāb al-yad (Arabic arithmetic: The Arithmetic of Abū al-Wafā’ al-Būzjānī). Amman: Jam’īat ‘ummāl al-maṭābi’ al-ta’āwunīyat.Google Scholar
Saidan, Ahmad S. 1974. The arithmetic of Abu’l-Wafā. Isis 65:367–75.Google Scholar
Saidan, Ahmad S. 1977a. Ed. Kitāb al-a’dād al-mutaḥābbat li-Thãbit ibn Qurra (Amicable numbers, by Thābit ibn Qurra). Amman: The Jordanian University.Google Scholar
Saidan, Ahmad S. 1977b. Ed. Kitāb tasṭīḥ al-ṣuwar wa tabṭīh al-kuwar li-Abi all-Rayḥān al-Bīrūnī. Dirāsāt (Amman: The Jordanian University) 4:7–22.Google Scholar
Saidan, Ahmad S. 1978a. The arithmetic of al-Uqlīdisī. The story of Hindu-Arabic arithmetic as told in Kitāb al-fuṣūl fī al-ḥisāb al-hindī by Abū al-Ḥasan Aḥmad ibn Ibrāhīm al-Uqlīdisī. Dordrecht: D. Reidel.Google Scholar
Saidan, Ahmad S. 1978b. Ḥawl khawāṣṣ al-a’dād li-Abī Ja’far, Muḥammad ibn al-Ḥusain (Theorems in number theory, by Abū Ja’far Muḥammad ibn al-Ḥusain). Dirāsāt (December), 7–49.Google Scholar
Saidan, Ahmad S. 1985. The Takmila fīal-ḥisāb by al-Baghdādī, . To appear in King and Saliba 1985.Google Scholar
Saliba, George A. 1973. The meaning of al-jabr wa’l-muqābalah. Centauras 17:189–204. Reprinted in Kennedy et al. 1983.Google Scholar
Saliba, George A. 1976. The double-argument tables of Cyriacus. Journal for the History of Astronomy. 7:41–46.Google Scholar
Saliba, George A. 1977a. Asālib ḥisābat al-jadāwal al-falakīyat al-islāmīyat. Proceedings of the First International Symposium for the History of Arabic Science, vol. 1 (papers in Arabic), 275–94. Aleppo: University of Aleppo Press.Google Scholar
Saliba, George A. 1977b. Computational techniques in a set of late medieval astronomical tables. Journal for the History of Arabic Science 1(1):24–32.Google Scholar
Sesiano, Jacques 1977a. Le traitement des equations indéterminées dans le Badī’ fī’l-ḥisāb d’Abū Bakr al-Karajī. Archive for History of Exact Sciences 17(4):297–379.Google Scholar
Sesiano, Jacques 1977b. Les méthodes d’analyse indéterminée chez Abū Kāmil. Centauras 21(2): 89–105.CrossRefGoogle Scholar
Sesiano, Jacques 1979. Note sur trois théorèmes de mécanique d’al-Quhi et leur conséquence. Centaurus 22(4):281–97.Google Scholar
Sesiano, Jacques 1980. Herstellungsverfahren magischer Quadrate aus islamischer Zeit (I). Sudhoffs Archiv 64(2):187–96.Google Scholar
Sesiano, Jacques 1981. Herstellungsverfahren magischer Quadrate aus islamischer Zeit (II). Sudhoffs Archiv 65(3):251–65.Google Scholar
Sesiano, Jacques 1982. Books IV to VII of Diophantus’ Arithmetica in the Arabic translation attributed to Qusṭā ibn Lūqā Heidelberg: Springer Verlag.Google Scholar
Sesiano, Jacques 1985. A treatise by al-Qabīṣī (Alchabitius) on arithmetical series. To appear in King and Saliba 1985.Google Scholar
Sezgin, Fuat 1974, 1978. Geschichte des arabischen Schrifttums. 5. Mathematik; 6. Astronomie. Leiden: E. J. Brill.Google Scholar
Suter, H. 1922. Über die Projektion der Sternbilder und der Länder von al-Bīrūnī. Abh. zur Gesch. der Naturwiss., Erlangen, 4:79–93.Google Scholar
Tee, Garry 1977. Letter to the editor: On computational techniques. Journal for the History of Arabic Science 1(2):323–24.Google Scholar
Tekeli, Sevim 1968. ‘The duplication of the cube’ Zail-i Tahrir al Uqlidas, Majmua’ and Muntahâ, Sidra al. In Proceedings of the 12th International Congress of the History of Science, 137–40. Paris.Google Scholar
Tichenor, Mark J. 1967. Late medieval two-argument tables for planetary longitudes. Journal of Near Eastern Studies 26:126–28. Reprinted in Kennedy et al. 1983.Google Scholar
Toomer, G. J. 1976. Diocles on burning mirrors: An Arabic translation of the lost Greek original. Heidelberg: Springer Verlag.Google Scholar
Villuendas, M. V. 1979. La trigonometria europea en el siglo XI: Estudio de la obra de ibn Mu’āḏ El kitāb mayhūlāt. Barcelona: Instituto de Historia de la Ciencia de la Real Academia de Buenas Letras.Google Scholar
Wieber, R. 1972. Das Schachspiel in der arabischen Literatur von den Anfangen bis zur zweiten Halfte des 16. Jahrhunderts. Dissertation, University of Bonn.Google Scholar
Woepcke, F. 1861. Recherches sur plusieurs ouvrages de Léonard de Pise. Atti dell’Academia Pontificia dei nuovi Lincei 14:211–27, 241–69, 301–24, 343–56.Google Scholar
Yadegari, Mohammed 1978. The binomial theorem described by Amir Kalan al-Bukhari circa 1297 AD. Islamic Quarterly 20–22:36–39.Google Scholar
Yadegari, Mohammed 1980. The binomial theorem: A widespread concept in medieval mathematics. Historia Mathematica 7:401–406.Google Scholar
De Young, Gregg 1981. The arithmetic books of Euclid’s Elements in the Arabic tradition. Ph.D. dissertation, Harvard University.Google Scholar
De Young, Gregg 1984. The Arabic textual traditions of Euclid’s Elements. Historia Mathematica 11:147–60.Google Scholar
Youschevitch, Adolf P. 1976. Les mathématiques arabes (VIIIe-XVe siècles). Trans. Cazenave, M. and Jaouiche, K.. Paris: J. Vrin.Google Scholar