3905Accesses
Abstract
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.
This is a preview of subscription content,log in via an institution to check access.
Access this chapter
Subscribe and save
- Get 10 units per month
- Download Article/Chapter or eBook
- 1 Unit = 1 Article or 1 Chapter
- Cancel anytime
Buy Now
- Chapter
- JPY 3498
- Price includes VAT (Japan)
- eBook
- JPY 11439
- Price includes VAT (Japan)
- Softcover Book
- JPY 14299
- Price includes VAT (Japan)
- Hardcover Book
- JPY 14299
- Price includes VAT (Japan)
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Ahmad, S., Rashed, R. (eds.), 1972. Al-Bāhir en algèbre d’as-Samawal. (In French and Arabic.) University Press of Damascus, Damascus.
Ali, J. (trans.), 1967. The Determination of the Coordinates of Cities. American University of Beirut Press, Beirut.
Anbouba, A., 1977. Construction de l’heptagone régulier par les Arabes au 4e siècle de l’hégire. Journal for the History of Arabie Science 1, 352–84.
——— 1978a. L’algèbre arabe aux IXe et Xe siècles, Aperçu général. Journal for the History of Arabie Science 2, 66–100.
——— 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 Anbouba 1977.)
——— 1979. Un traité d’Abū Jacfar (al-Khāzin) sur les triangles rectangles numériques. Journal for the History of Arabie Science 3, 134–78.
——— 1982. Un mémoire d’al-Qabīsī (4e siècle h.) sur certaines sommations numériques. Journal for the History of Arabie Science 6, 208–81.
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.
——— , 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. Academy of the Socialist Republic of Romania, Bucharest.
——— , 1981b. An anonymous treatise on the regular nonagon. Journal for the History of Arabic Science 5, 37–41.
——— , 1982. Al-Bīrūnī on plane maps of the sphere. Journal for the History of Arabic Science 6, 47–112.
——— , 1985. On the origins of al- Bīrūnī ’s ’Method of the Zījes’ in the theory of sundials. Centauras 28, 1–16. (Editors: In the original paper the details were given as "to appear." We have supplied the full reference.)
——— , 1987. Spherical trigonometry in the zīj of Kūshyār ibn Labbān. In: King, D.A., Saliba, G. (eds.), From Deferent to Equant: A Volume of Studies in the History of Science in the Ancient and Medieval Near East in Honor of E.S. Kennedy, New York Academy of Sciences, New York, pp. 15–33. (Editors: We have supplied the full reference.)
Bulgakov, P.G. (ed.), 1962. Tahdīd nihāyāt al-amākin li-tashīh masāfāt al-masākin. Published in Majallat machad al-makhtūtāt al-carabiyya. The Arab League, Cairo.
Busard, H.L.L., van Konigsveld, P.S., 1973. Der Liber de arcibus similibus des Ahmed ibn Jusuf. Annals of Science 30, 381–406.
De Young, G., 1981. The Arithmetic Books of Euclid’s Elements in the Arabic Tradition. Ph.D. dissertation, Harvard University.
——— , 1984. The Arabic textual traditions of Euclid’s Elements. Historia Mathematica 11, 147–60.
Debarnot, M.-Th., 1978. Introduction du triangle polaire par Abu Nasr b. cIrāq. Journal for the History of Arabic Science 2, 126–36.
——— , 1980. Les Clefs d’astronomie d’Abū al-Rayhān … al-Bīrūnī : La trigonometrie sphérique chez les arabes de l’est à la fin du Xe siècle. Thèse du 3eme cycle. Paris.
Djebbar, A., 1981. Enseignement et recherche mathématiques dans le Maghreb des XIIIe- XIVe siècles. Publications mathématiques d’Orsay. Université de Paris-Sud, Paris.
——— , 1985. L’analyse combinatoire au Maghreb : l’example d’ibn Muncim (XIIe- XIIIe siècles). Publications mathématiques d’Orsay. Université de Paris-Sud, Paris.
Ehrenkreutz, A.S., 1962. The kurr system in medieval Iraq. Journal of the Economie and Social History of the Orient 5, 309–314.
——— , 1964. The tasrīf and Tas’īr calculations in medieval Mesopotamian fiscal operations. Journal of the Economic and Social History of the Orient 7, 46–56.
Engroff, J.W., 1980. The Arabic tradition of Euclid’s Elements, Book V. Ph.D. dissertation, Harvard University.
Gandz, S., 1938. The algebra of inheritance. Osiris 5, 319–91.
Hamadanizadeh, J., 1976. Medieval interpolation theory. Ph.D. dissertation, Teacher’s College, Columbia University.
——— , 1978. Interpolation schemes in Dastūr al-Munajjimīn. Centaurus 2,44–52.
——— , 1980. The trigonometric tables of al-Kāshī in his Zīj-i Khāqānī. Historia Mathematica 7, 38–45.
Hartner, W., 1965. Al-Djabr wa’1-mukābala. In: Encyclopedia of Islam, ed. 2, vol. 2. E.J. Brill, Leiden, pp. 360–62.
Hermelink, H., 1975. The earliest reckoning books existing in the Persian language. Historia Mathematica 2, 299–303.
——— , 1978. Arabische Unterhaltungsmathematik als Spiegel jahrtausendealter Kulterbeziehungen zwischen Ost und West. Janus 65, 105–17.
Hochheim, A. (trans.), 1877–1880. Al-Kāfī fi hisāb. 3 pts. Halle/Saale.
Hogendijk, J.P., 1981. How trisections of the angle were transmitted from Greek to Islamic geometry. Historia Mathematica 8, 417–38.
——— , 1984a. Ibn al-Haytham’s Completion of the Conies. Springer-Verlag, New York.
——— , 1984b. Greek and Arabic constructions of the regular heptagon. Archive for History of Exact Sciences 30, 197–330.
——— , 1985. Thābit ibn Qurra and the pair of amicable numbers 17296, 18416. Historia Mathematica 12,269–273. (Editors: We have completed the reference.)
Irani, R.A.K., 1956. The Jadwal al-taqwīm of Habash al-Hāsib. Unpublished M.A. thesis, American University of Beirut.
Jaouiche, K. (ed. and trans.), 1976. Le livre du qarastūn de Tābit ibn Qurra. E. J. Brill, Leiden.
Jensen, C., 1971. Abū Nasr Mansūr’s approach to spherical astronomy as developed in his treatise "The table of minutes." Centaurus 16, 1–19.
Kennedy, E.S., 1968. The exact sciences in Iran under the Saljuqs and Mongols. In: Boyle, J.A. (ed.), Cambridge History of Iran, Volume 5. Cambridge University Press, Cambridge, 659–679.
——— , 1969. An overview of the history of trigonometry. In: Baumgart, J.K. (ed.), Historical Topics for the Mathematics Classroom. National Council of Teachers in Mathematics, Washington, D.C., pp. 333–359. Reprinted in Kennedy et al., 1983.
——— , 1970. The Arabic heritage in the exact sciences. Al-Abhath 23, 327–344. Reprinted in Kennedy et al., 1983.
——— , 1973. A commentary upon Biruni’s Kitāb tahdīd al-amākin. University of Beirut Press, Beirut.
——— , 1976. The Exhaustive Treatise on Shadows by Abū al-Rayhān al-Bīrūnī. vol. 1, trans., vol. 2, commentary. Institute for History of Arabic Science, Aleppo.
——— , 1984. Applied mathematics in the tenth century: Abu’l-Wafā’ calculates the distance Baghdad-Mecca. Historia Mathematica 11, 193–206.
Kennedy, E.S., et al., 1983. Studies in the Islamic exact sciences. American University of Beirut Press, Beirut.
Kennedy, E.S., Debarnot, M.-Th., 1984. Two mappings proposed by Bīrūnī. Zeitschrift fur Geschichte der arabisch-islamischen Wissenschaften 1, 145–147. (Editors: We have completed the reference.)
King, D.A., 1972. The astronomical works of Ibn Yunus. Ph.D. dissertation, Yale University.
——— , 1973. Al-Khalīlīs auxiliary tables for solving problems of spherical astronomy. Journal for the History of Astronomy 4, 99–110.
——— , 1974a. On medieval multiplication tables. Historia Mathematica 1, 317–23. Reprinted in King 1985a.
——— , 1974b. An analog computer for solving problems of spherical astronomy. Archives internationales d’histoire des sciences 24, 219–242. Reprinted in King 1986.
——— , 1979a. Notes on the sources for the history of early Islamic mathematics. Journal of the American Oriental Society 99, 450–59.
——— , 1979b. Kibla. In: Encyclopedia of Islam, ed. 2, vol. 5, pp. 83–88. E. J. Brill, Leiden.
——— , 1979c. Supplementary notes on medieval Islamic multiplication tables. Historia Mathematica 6, 405–417. Reprinted in King 1985a.
——— , 1980. The exact sciences in medieval Islam: Some remarks on the present state of research. Middle East Studies Association Bulletin 14, 10–26.
——— , 1981–1986. A catalog of the scientific manuscripts in the Egyptian National Library. 2 vols. American Research Center in Egypt, Cairo.
——— , 1981. Universal solutions in medieval Islamic astronomy. Abstract of talk, in Proceedings of the 16th International Congress of the History of Science, Part A., 144. Academy of the Socialist Republic of Romania, Bucharest.
——— ., 1983a. The astronomy of the Mamluks. Isis 74, 531–555. Reprinted in King 1985a.
——— , 1983b. Al-Khwārizmī and new trends in mathematical astronomy in the ninth century. Hagop Kevorkian Center for Near Eastern Studies, New York University, New York.
——— , 1984. A Survey of the Scientific Manuscripts in the Egyptian National Library. Undena Publication, Malibu, California.
——— 1985a. Islamic Mathematical Astronomy. London, Variorum Reprints.
——— , 1985b. Some early Islamic approximate methods for determining the Qibla. To appear in King and Saliba 1985. (Editors: This paper was, apparently, not published in this form. King’s contribution to this collection was: Some early Islamic tables for determining lunar crescent visibility. In: King, D.A., Saliba, G. (eds.), 1987, From Deferent to Equant: A Volume of Studies in the History of Science in the Ancient and Medieval Near East in Honor of E.S. Kennedy, New York Academy of Sciences, New York, pp. 185–225.)
——— 1986. Islamic Astronomical Instruments. Variorum Reprints, London.
King, D.A., Saliba, G.A. (eds.), 1987. From Deferent to Equant: Studies in the History of Science in the Ancient and Medieval Near East in Honor of E.S. Kennedy. New York Academy of Sciences, New York. (Editors: In the original article, this book was noted as "to appear." We have supplied the published details.)
Knorr, W, 1983. On the transmission of geometry from Greek into Arabic. Historia Mathematica 10, 71–78.
Lorch, R., 1984. Qibla diagrams and associated instruments. To appear. (Editors: We have not found a 31 published version of this paper.)
——— 1987. Al-Saghānī’s treatise on projecting the sphere. In: King, D.A., Saliba, G. (eds.), From Deferent to Equant: A Volume of Studies in the History of Science in the Ancient and Medieval Near East in Honor of E.S. Kennedy, New York Academy of Sciences, New York, pp. 237–252. (Editors: We have supplied the published details.)
Luckey, P., 1951. Die Rechenkunst bei Ğamsīd b. Mascud al-Kāshī. Abhandlungen fur die Kunde des Morgenlandes, Deutsche Morgenlandische Gesellschaft 31, Wiesbaden.
Mach, R., 1977. Catalogue of Arabie manuscripts (Yahuda Collection) in the Garrett Collection, Princeton University. Indexed by R.D. McChesney. Princeton University Press, Princeton.
Matvievskaya, G., 1987. The theory of quadratic irrationals in medieval oriental mathematics. In: King, DA., Saliba, G. (eds.), From Deferent to Equant: A Volume of Studies in the History of Science in the Ancient and Medieval Near East in Honor of E.S. Kennedy, New York Academy of Sciences, New York, pp. 419–426. (Editors: We have supplied the published details.)
Muwafi, A., Philippou, A.N., 1981. An Arabic version of Eratosthenes on mean proportionals. Journal for the History of Arabic Science 5, 147–74.
Naini, A.D., 1982. Geschichte der Zahlentheorie im Orient. Verlag Klose and Co., Braunschweig.
Plooij, E.B., 1950. Euclid’s conception of ratio … as criticized by Arabian commentators. Ph.D. dissertation, Rijksuniversiteit te Leiden.
Rashed, R., 1972. L’induction mathématique : al-Karajī, as-Samaw’al. Archive for History of Exact Sciences 9, 1–21.
——— 1973. Algèbre et linguistique : l’analyse combinatoire dans la science arabe. In: Cohen, R. (ed.), Boston Studies in the Philosophy of Sciences. D. Reidei, Dordrecht, pp. 383–99.
——— 1974. Résolution des equations numériques et algèbre : Šaraf-al-Din al-Tūsī, Viète. Archive for History of Exact Sciences 12, 244–90.
——— 1975a. Ed. L’art de l’algèbre de Diophante. Matabi1 al-hai’a al-misriyya d-’amma al-kitib, Cairo.
——— 1975b. Récommencements de l’algèbre au XIe et XIIe siècles, In: Murdoch, J.E., Sylla, E.D. (eds.), The Cultural Context of Medieval Learning. D. Reidei, Dordrecht, pp. 33–60.
——— 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.
——— 1979a. L’analyse diophantienne au Xe siècle : l’exemple d’al-Khāzin, Revue d’histoire des sciences 32, 193–222. Reprinted in Rashed 1984a.
——— 1979b. La construction de l’heptagone régulier par Ibn al-Haytham. Journal for the History of Arabie Science, 3, 309–87.
———1980. Ibn al-Haytham et le théorème de Wilson, Archive for History of Exact Sciences 22, 305–21. Reprinted in Rashed 1984a.
——— 1983. Nombres amiables, parties aliquotes et nombres figurés auXIIleme-XIVeme siècles. Archive for History of Exact Sciences 28, 107–47. Reprinted in Rashed 1984a.
——— 1984a. Entre arithmétique et algèbre : recherches sur l’histoire des mathématiques arabes. Les Belles Lettres, Paris.
——— (ed. and trans.) 1984b. Diophante : les arithmétiques. Tome III (livre IV), tome IV (livres V, VI, VII). Les Belles Lettres, Paris.
Rashed, R., Djebbar, A., 1981. L’Œuvre algébrique d’al-Khayyam. Institute for the History of Arabie Science, Aleppo.
Richter-Bernburg, L., 1982. Al-Bīrūnī’s Maqāla fī tastīh al-suwar wa-tabtīkh al-kuwar. Journal for the History of Arabie Science 6, 113–22. 32
Rosenfeld, B.A., 1978. Review of Fuat Sezgin’s Geschichte des arabischen Schrifttums, Bd. 5. Archives internationales d’histoire des sciences, 28, 325–29.
Rozhanskaya, M., 1987. On a mathematical problem in al-Khāzinī’s Book of the Balance of Wisdom. In: King, D.A., Saliba, G. (eds.), From Deferent to Equant: A Volume of Studies in the History of Science in the Ancient and Medieval Near East in Honor of E.S. Kennedy, New York Academy of Sciences, New York, pp. 427–435. (Editors: We have supplied the full reference.)
Rozhanskaya, M., Rosenfeld, B.A., 1987. On al-Bīrūnī’s Densimetry. In: King, D.A., Saliba, G. (eds.), From Deferent to Equant: A Volume of Studies in the History of Science in the Ancient and Medieval Near East in Honor of E.S. Kennedy, New York Academy of Sciences, New York, pp. 404–417. (Editors: We have supplied the full reference.)
Sabra, A.I., 1968. Thābit ibn Qurra on Euclid’s parallels postulate. Journal of the Warburg and Courtauld Institutes 31, 12–32.
——— 1969. Simplicius’s proof of Euclid’s parallels postulate. Journal of the Warburg and Courtauld Institutes 32, 1–24.
——— 1971. Ilm al-hisāb. In Encyclopedia of Islam, ed. 2, vol. 3, 1138–1141.
——— 1982. Ibn al-Haytham’s lemmas for solving ’Alhazens problem.’ Archive for History of Exact Sciences 26, 299–324.
——— 1983. Ed. Kitāb al-manāzir (The Optics of Ibn al-Haytham). Arabic text of books 1,2, and 3 on direct vision. National Council for Culture, Arts, and Letters, Arabic Heritage Department, Kuwait.
——— 1966. The earliest extant Arabic arithmetic. Isis 57, 475–90. See also Saidan 1978a.
——— (ed.) 1971. cIlm al-hisāb al-cArabī: hisāb al-yad (Arabic arithmetic: The Arithmetic of Abū al-Wafā’ al-Būzjānī). Jamcīat cummāl al-matābi’ al-tacā-wunīyat, Amman.
——— 1974. The arithmetic of Abu’1-Wafā. Isis 65, 367–75.
——— (ed.) 1977a. Kitāb al-a’dād al-mutahābbat li-Thābit ibn Qurra (Amicable numbers, by Thābit ibn Qurra). The Jordanian University. Amman.
——— (ed.) 1977b. Kitāb tastīh al-suwar wa tabtīh al-kuwar li-Abi all-Rayhān al-Bīrūnī. Dirāsāt. The Jordanian University (Amman) 4, 7–22.
——— 1978a. The arithmetic of al-Uqlīdisī. The story of Hindu-Arabic arithmetic as told in Kitāb al-fusūl fī al-hisāb al-hindī by Abū al-Hasan Ahmad ibn Ibrāhim al-Uqlīdisī. D. Reidei, Dordrecht.
——— 1978b. Hawl khawāss al-acdād li-Abī Jacfar, Muhammad ibn al-Husain (Theorems in number theory, by Abū Jacfar Muhammad ibn al-Husain), Dirāsāt (December), 7–49.
——— 1987. The Tafanila fī al-hisāb by al-Baghdādī. In: King, D.A., Saliba, G. (eds.), From Deferent to Equant: A Volume of Studies in the History of Science in the Ancient and Medieval Near East in Honor of E.S. Kennedy, New York Academy of Sciences, New York, pp. 437–443. (Editors: We have supplied the full reference.)
——— 1973. The meaning of al-jabr wa’1-muqābalah. Centaurus 17, 189–204. Reprinted in Kennedy et al. 1983.
——— 1976. The double-argument tables of Cyriacus. Journal for the History of Astronomy 7,41–46.
——— 1977a. Asālib hisābat al-jadāwal al-falakīyat al-islāmīyat. Proceedings of the First International Symposium for the History of Arabic Science, vol. 1 (papers in Arabic). University of Aleppo Press, Aleppo, pp. 275–94.
——— 1977b. Computational techniques in a set of late medieval astronomical tables. Journal for the History of Arabic Science, 1, 24–32.
Sesiano, J., 1977a. Le traitement des equations indéterminées dans le Badīc fī’1-hisāb d’Abū Bakr al-Karajī. Archive for History of Exact Sciences 17, 297–379.
——— 1977b. Les méthodes d’analyse indéterminée chez Abūu Kāmil. Centaurus 21, 89–105.
——— 1979. Note sur trois théorèmes de mécanique d’al-Quhi et leur conséquence. Centaurus 22, 281–97.
——— 1980. Herstellungsverfahren magischer Quadrate aus islamischer Zeit (I). Sudhoffs Archiv 64, 187–96.
——— 1981. Herstellungsverfahren magischer Quadrate aus islamischer Zeit (II). Sudhoffś Archiv 65, 33 251–65.
——— 1982. Books IV to VII of Diophantus’ Arithmetica in the Arabie translation attributed to Qustā ibn Lūqā. Springer Verlag, New York.
——— 1987. A treatise by al-Qabīsī (Alchabitius) on arithmetical series. In: King, D.A., Saliba, G (eds.), From Deferent to Equant: A Volume of Studies in the History of Science in the Ancient and Medieval Near East in Honor of E.S. Kennedy, New York Academy of Sciences, New York, pp. 483–500. (Editors: We have supplied the full reference.)
Sezgin, F., 1974, 1978. Geschichte des arabischen Schrifttums. 5. Mathematik; 6. Astronomie. E. J. Brill, Leiden.
Suter, H., 1922. Über die Projektion der Sternbilder und der Lānder von al-Blrüm. Abhandlungen zur Geschichte der Naturwissenschaften und der Medizin, Erlangen 4, 79–93.
Tee, G., 1977. Letter to the editor: On computational techniques. Journal for the History of Arabic Science 1, 323–24.
Tekeli, S., 1968. ’The duplication of the cube’ Zail-i Tahrir al Uqlidas, Majmuac and Sidra al Muntahâ, In Proceedings of the 12th International Congress of the History of Science, Paris, pp. 137–40.
Tichenor, M.J., 1967. Late medieval two-argument tables for planetary longitudes. Journal of Near Eastern Studies 26, 126–28. Reprinted in Kennedy et al. 1983.
Toomer, G.J., 1976. Diocles on Burning Mirrors: An Arabic Translation of the Lost Greek Original. Springer-Verlag, New York.
Villuendas, M.V., 1979. La trigonometria europea en el siglo Xl: Estudio de la obra de ibn Mu’ad El kitāb mayhūlāt. Instituto de Historia de la Ciencia de la Real Academia de Buenas Letras, Barcelona.
Wieber, R., 1972. Das Schachspiel in der arabischen Literatur von den Anfangen bis zur zweiten Halfte des 16 Jahrhunderts. Ph.D. dissertation, University of Bonn.
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.
Yadegari, M., 1978. The binomial theorem described by Amir Kalan al-Bukhari circa 1297 a.d. Islamic Quarterly, 20–22, 36–39.
——— 1980. The binomial theorem: A widespread concept in medieval mathematics. Historia Mathematica, 7, 401–406.
Youschevitch, A.P., 1976. Les mathématiques arabes (VIIIe-XVc siècles), Cazenave, M., Jaouiche, K. (trans.). J. Vrin, Paris.
Author information
Authors and Affiliations
British Columbia, Canada
J. Lennart Berggren
- J. Lennart Berggren
You can also search for this author inPubMed Google Scholar
Editor information
Editors and Affiliations
School for International Liberal Studies, Waseda University, Tokyo, Japan
Nathan Sidoli
Quest University, Squamish, British Columbia, Canada
Glen Van Brummelen
Rights and permissions
Copyright information
© 2014 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Berggren, J.L. (2014). History of Mathematics in the Islamic World: The Present State of the Art [1985]. In: Sidoli, N., Van Brummelen, G. (eds) From Alexandria, Through Baghdad. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36736-6_4
Download citation
Published:
Publisher Name:Springer, Berlin, Heidelberg
Print ISBN:978-3-642-36735-9
Online ISBN:978-3-642-36736-6
eBook Packages:Mathematics and StatisticsMathematics and Statistics (R0)
Share this chapter
Anyone you share the following link with will be able to read this content:
Sorry, a shareable link is not currently available for this article.
Provided by the Springer Nature SharedIt content-sharing initiative