Abstract
This paper surveys work done over the past decade, largely in Western Europe and North America, in the history of the mathematical sciences as practiced in medieval Islam from central Asia to Spain. Among the major topics covered, in addition to the usual branches of mathematics, are mathematical geography, astronomy, and optics. We have also given accounts of some current debates on the interpretation ofimportant texts and, in addition, we havesu rveyed some of the literature dealing with the interrelation of mathematics and society in medieval Islam.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Aballagh, M., Djebbar, A., 1987. Découverte d'un écrit mathématique d'al-Haşşār (XIIe S.) : Le livre I du Kāmil. Historia Mathematica 14, 147–158.
Abgrall, P., 1995. Les cercles tangents d'al-Qūhī. Arabie Sciences and Philosophy 5, 263–295.
Ağargün, A.G., Fletcher, CR., 1994. Al-Fārisī and the Fundamental Theorem of Arithmetic. Historia Mathematica 21, 162–173.
Anagnostakis, C, 1987. How to divide the ecliptic on an astrolabe. In: [12, pp. 133–144].
Bebbouchi, R., 1990. L'infini et les mathématiciens arabes. Deuxième colloque maghrébin sur l'histoire des mathématiques arabes : Tunis, les 1–2-3 Décembre 1988, Actes du colloque. University of Tunis, Tunis, pp. 20–26.
Bellosta, H., 1991. Ibrāhīm ibn Sinān: On Analysis and Synthesis. Arabic Sciences and Philosophy 1,211–232.
Berggren, J.L., 1982. Al-Bīrūnī on plane maps of the sphere. Journal for the History of Arabic Science 6, 47–96.
——— 1985. The origin of al-Bīrūnī's "method of the zījes" in the theory of sundials. Centauras 28, 1–16.
——— 1985. History of mathematics in the Islamic world: The present state of the art. Middle East Studies Association Bulletin 19, 9–33.
——— 1986. Episodes in the Mathematics of Medieval Islam. Springer-Verlag, New York.
Berggren, J.L., Goldstein, B.R. (eds.), 1987. From Ancient Omens to Statistical Mechanics: Essays in the Exact Sciences Presented to Asger Aaboe. Munksgaard, Copenhagen.
Berggren, J.L., 1991. Medieval Islamic methods for drawing azimuth circles on the astrolabe. Centauras 34, 309–344.
——— 1991\1992. Habash's analemma for representing azimuth circles on the Astrolabe. Zeitschrift für Geschichte der arabisch-islamischen Wissenschaften 7, 23–30.
——— 1992. Greek and Islamic elements in Arabic mathematics. In: Mueller, I. (ed.), Π?ΡΙ ΤΩN ΜAΘHΜAΤΩN. Academic Print Publications, Edmonton, Alberta, pp. 195–217.
——— 1987. Archimedes among the Ottomans. In: [12, pp. 101–109].
——— 1994. Abū Sahl Al-Kūhī's Treatise on the Construction of the Astrolabe with Proof: Text, translation and commentary. Physis 31, 141–252.
——— 1995. Review of The Optics of Ibn al-Haytham, Books I—III: On Direct Vision. Physis 32, 143–153.
——— 1996. Al-Kuhī's "Filling a Lacuna in Book II of Archimedes" in the version of Nasīr al-Dīn al-Tūsī. Centauras 38, 140–207.
Brentjes, S., 1992. Der Thābit ibn Qurra zugeschriebene Zusatz I, 46 zu Euklid I, 46 in MS Leiden 399, 1. In: [37, pp. 91–120].
——— 1993. Varianten einer-Hağğāğ-Version von Buch II der Elemente. In: [52, pp. 47–67].
——— 1994. Textzeugen und Hypothesen zum arabischen Euklid in der Überlieferang von al-Hağğāğ ibn Yūsuf ibn Maţar (zwischen 786 und 833). Archive for History of Exact Sciences 47, 53–92.
——— 2007. Reflections on the role of the exact sciences in Islamic culture and education between the twelfth and the fifteenth centuries. In: Abattouy, M. (ed.), Études d'histoire des sciences arabes: textes réunis et présentés. Fondation du roi Andul-Aziz Al Saoud, Casablanca, pp. 15–33. (Editors: In the original paper, the details of this reference are given as "unpublished preprint." We have suppled the details.)
Butzer, PL, Lohrmann, D. (eds.), 1993. Science in Western Civilization in Carolingian Times. Basel, Birkhäuser. |
Calvo, E., 1992. Ibn Bāşo's universal plate and its influence on European astronomy. Scientiaram Historia 18, 61–69.
——— 1992–1994. On the construction of Ibn Bāşo's universal astrolabe (14th c.) according to a Moroccan astronomer of the 18th century. Journal for the History of Arabic Science 10, 53–67.
Carandell, J., 1984. An analemma for the determination of the azimuth of the qibla in the Risālā fī cilm al-zilāl of Ibn al-Raqqām. Zeitschrift für Geschichte der arabisch-islamischen Wissenschaften 1, 61–72.
Chabás, J., Goldstein, B.R., 1994. Andalusian astronomy: al-Zīj al-Muqtabis of Ibn al-Kammād. Archive for History of Exact Sciences 48, 1–41.
Chemia, K., 1994. Similarities between Chinese and Arabic mathematical writings: (I) Root extraction. Arabic Sciences and Philosophy 4, 207–266.
Chemia, K., Djebbar, A., Mazars, G., 1992. Mondes arabe, chinois, indien : Quelques points communs dans le traitement des nombres fractionnaires. In: [175, pp. 263–276].
Comes, M., 1991. Ecuatorios andalusies : Ibn al-Samh, al-Zarqālluh y Abū-1-Şalt. Universidad de Barcelona, Barcelona.
Crossley, J.N., Henry, A.S., 1990. Thus spake al-Khwārizmī: A translation of the Cambridge University Library ms. Ii.vi.5. Historia Mathematica 17, 103–131.
Crozet, P., 1993. L'idée de dimension chez al-Sijzī. Arabie Sciences and Philosophy 3, 251–286.
Dallai, A., 1984. Al-Bīrūnī on climates. Archives internationales d'histoire des sciences 34, 3–18.
——— 1988. Bīrūnīs Book of Pearls Concerning the Projection of Spheres. Zeitschrift für Geschichte der arabisch-islamischen Wissenschaften 4, 81–138.
Dallai, A., 1995. Ibn al-Haytham's universal solution for finding the direction of the qibla by calculation. Arabic Sciences and Philosophy 5, 145–194.
Demidov, S.S., Folkerts, M., Rowe, D.E., Scriba, CJ. (eds.), 1992. Amphora, Festschrift for Hans Wussing on the Occasion of his 65th Birthday. Birkhäuser, Basel.
Dhanani, A., 1994. The physical theory of kalam: Atoms, space, and void in Basrian Muctazili Cosmology. Brill, Leiden and New York.
Dhanani, A., 1981. L'analyse combinatoire dans l'enseignement d'Ibn Muncim, XIIe-XIIIe siècles. Université de Paris-Sud, Département de mathématiques.
——— 1996. Quelques commentaires sur les versions arabes des Eléments d'Euclide et sur leur transmission à l'Occident musulman. In: [176, 91–114].
——— 1995. Le traitement des fractions dans la tradition mathématique arabe du Maghreb. In: [175, pp. 263–276].
——— 1988. Quelques aspects de l'algèbre dans la tradition mathématique arabe de l'Occident musulman. Actes du premier colloque Maghrébin d'Alger sur les mathématiques arabes. Maison du Livre, Alger, pp. 99–123.
——— 1995. Mathematics in Medieval Maghreb. AMUCHMA Newsletter 15, 3–42. [Published by the African Mathematical Union]
——— 1998. La tradition arithmétique euclidienne dans le Kitāb Al-htikmāl d'Al-Mu' taman et son prolongement en Andalus. Veme Colloque Maghrebim sur l'histoire des mathématiques arabes : Actes du colloque, Hammamet 1–2-3 Décembre 1994. L'Association Tunisienne des Sciences Mathématiques, Tunis, pp. 62–84. (Editors: In the original paper, the date of this reference is given as "to appear." We have suppled the final details.)
Dold-Samplonius, Y., 1987. Developments in the solution to the equation cx 2 + bx = a from al-Khwārizmī to Fibonacci. In: [88, pp. 71–87].
——— 1990. Quadratic equations in Arab mathematics. In: Balmer, H., Glaus, B. (eds.), Die Blütezeit der arabischen Wissenschaft. Verlag der Fachvereine, Zürich, pp. 67–78.
——— 1992. Practical Arabic mathematics: Measuring the muqarnas by al-Kāshī. Centauras 35, 193–242. I
——— 1992. The XVth century Timurid mathematician Ghiyāth al-Dīn Jamshīd al-Kāshī and his computation of the qubba. In: [37, pp. 171–181].
——— 1993. The volume of domes in Arabic mathematics. In: [52, pp. 93–106].
Farès, N., 1995. Le calcul du maximum et la 'dérivée' selon Sharaf al-Dīn al-Tūsī. Arabie Sciences and Philosophy 5, 219–238.
Folkerts, M., 1997. Die älteste lateinische Schrift über das indische Rechnen nach al-Hwārizmī: Edition, Übersetzung und Kommentar. Bayerische Akademie der Wissenschaften, Philosophisch-historische Klasse, Abhandlungen (Neue Folge) Heft 113, Verlag der Bayerischen Akademie der Wissenschaften, München.
Folkerts, M., Hogendijk, J.P. (eds.),, 1993. Vestigia Mathematica: Studies in Medieval and Early Modern Mathematics in Honour of H.L.L. Busard. Rodopi, Amsterdam.
Hamadanizadeh, J., 1987. A survey of medieval Islamic interpolation schemes. In: [88, pp. 143–152].
Harley, J.B., Woodward, D. (eds.), 1992. The History of Cartography, vol. 2, book 1 : Cartography in the Traditional Islamic South Asian Societies. University of Chicago Press, Chicago.
Ibn al-Haytham, Abū cAlī al-Hasan ibn al-Hasan, 1983. Kitāb al-Manāzir, Books I—III On Direct Vision, Sabra, A. I. (ed.). National Council for Culture, Arts and Letters, Kuwait.
Herz-Fischler, R., 1988. Theorem xiv,** of the First "Supplement" to The Elements. Archives internationales d'histoire des sciences 38, 3–66.
Hogendijk, J.P., 1985. Al-Kuhī's construction of an equilateral pentagon in a given square. Zeitschrift für Geschichte der arabisch-islamischen Wissenschaften 1, 100–144.
——— 1985. Thābit ibn Qurra and the pair of amicable numbers 17296, 18416. Historia Mathematka 12, 269–273.
——— 1986. Arabic traces of lost works of Apollonius. Archive for History of Exact Sciences 35, 187–253.
——— 1987. On Euclid's lost Porisms and its arabic traces. Bollettino di storia delle scienze matematiche 7, 93–115.
——— 1987. Review of La théorie des parallèles en pays d'Islam. Centauras 30, 293–294.
——— 1987. New light on the lunar crescent visibility table of Yacqūb Ibn Ţāriq. Journal of Near Eastern Studies 47, 95–103.
——— 1989. The mathematical structure of two Islamic astronomical tables for "Casting the Rays." Centauras 32, 171–202.
——— 1989. Sharaf al-Dīn al-Tūsī on the number of positive roots of cubic equations. Historia Mathematica 16, 69–85.
——— 1991. The geometrical parts of the Istikmāl of Yūsuf Al-Mu'taman Ibn Hūd (11th century): An analytical table of contents. Archives internationales d'histoire des sciences 41,207–281.
——— 1991. Al-Khwārizmī's table of the "sine of the hours" and the underlying sine table. Historia Scientiarum 42, 1–12.
——— 1993. The Arabic version of Euclid's On Division. In: [52, pp. 143–162].
——— 1994. Le traité d'Ibn al-Haytham sur les lignes horaires. Cahier du séminaire Ibn al-Haytham 4, 5–7.
——— 1994. Pure mathematics in Islamic civilization. In: Grattan-Guinness, I., (ed.), Companion Encyclopaedia of the History and Philosophy of the Mathematical Sciences. Routledge, London and New York, pp. 70–79.
——— 1994. The qibla table in the Ashrafī Zīj. In: [159, pp. 81–96].
Нøyryp, J., 1986. Al-Khwărizmĭ, Ibn Turk, and the Liber Mensurationum: On the origins of Islamic algebra. Erdem 5, 445–484.
——— 1987. The formation of "Islamic mathematics": Sources and conditions. Science in Context 1, 281–329.
Houzel, C, 1995. Sharaf al-Dīn al-Tūsī et le polygone de Newton. Arabie Sciences and Philosophy 5, 239–262.
Hughes, B., 1994. Problem-solving by Ajjūb al-Başrī: An early algebraist. Journal for the History of Arabic Sciences 10, 31–40.
Thābit Ibn Qurrā, 1987. Oeuvres astronomiques. (Régis, M., éd., trad, et comm.) Les Belles Lettres, Paris.
Jaouiche, K., 1986. La théorie des parallèles en pays d'Islam. Vrin, Paris.
——— 1988. L'analyse et la synthèse dans les mathématiques arabo-islamiques : Le livre d'Ibn al-Haytham. Histoire des mathématiques arabes. Maison des Livres, Algiers, pp. 106–124.
Kennedy, E.S., 1985. Spherical astronomy in Kāshī's Khāqānī Zīj. Zeitschrift für Geschichte der arabisch-islamischen Wissenschaften 2, 1–46.
Kennedy, E.S., Kennedy, M.H., 1987. Geographical Coordinates of Localities from Islamic Sources. Institut für Geschichte der arabisch-islamischen Wissenschaften, Frankfürt am Main.
Kennedy E.S., Saliba, G., 1991. The spherical case of the Tūsī couple. Arabic Sciences and Philosophy 1, 285–291.
Kennedy, E.S., 1994. The prime vertical method for the astrological houses as presented in Kāshī's Khāqāni Zīj. In: [159, pp. 95–97].
——— 1994. Ibn Mucādh on the astrological houses. Zeitschrift für Geschichte der arabisch-islamischen Wissenschaften 9, 153–160.
Kennedy, E.S., Lorch, R.P., 1997. Habash al-Hāsib on the melon astrolabe. In: Anellis, I.H., Demidov, S.S., Drucker, T., Hogendijk, J.P. (eds.), Mathematics, Past Tense Present: Festschrift on the History of Mathematics in Honor of Boris Rosenfeld's 80th Birthday. Modern Logic Publishing, Ames, LA.
Kheirandish, E., 1994. Review of The Optics of Ibn al-Haytham, Books I—III: On Direct Vision. Harvard Middle Eastern and Islamic Review 1, 188–194.
——— 1996. The Arabic "version" of Euclidean Optics: Transformations as linguistic problems. In: [177, pp. 227–246].
——— 1998. The Arabic Tradition of Euclid's Optics (Kitāb Uqlīdis fī Ikhtilāf al-manāzir). Springer-Verlag. New York. (Editors: In the original paper this item was "to appear." We have modified the reference to agree with the published book.)
King, D.A., 1986. The earliest Islamic mathematical methods and tables for finding the direction of Mecca. Zeitschrift für Geschichte der arabisch-islamischen Wissenschaften 3, 82–149.
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.
King, D.A., 1988. A medieval Arabic report on algebra before al-Khwārizmī. Al-Masāq 1,25–32.
——— 1990. A survey of medieval Islamic shadow schemes for simple time-reckoning. Oriens 32, 191–249.
——— 1990. An overview of the sources for the history of astronomy in the medieval Maghrib. Deuxième colloque maghrébin sur l'histoire des mathématiques arabes : Tunis, les 1–2-3 Décembre 1988, Actes du colloque. University of Tunis, Tunis, pp. 125–157.
——— 1990. Astronomy. In [163, pp. 274–289].
——— 1994. Astronomical Instruments between East and West, Kommunikation zwischen Orient und Okzident, Alltag und Sachkultur. Sitzungsberichte der Osterreichische Akademie der Wissenshaften, Philosophisch-Historische Klasse, 619. Band, Verlag der Akademie der Wisssen-schaften, Wien, 143–198. |
——— 1992. The ciphers of the monks and the astrolabe of Berselius reconsidered. In: [37, pp. 375–388].
——— 1994. Ein vergessenes Zahlensystem des mittelalterlichen Mönchtums. In: [159, pp. 405–420].
——— 1994. World-maps for finding the direction and distance of Mecca: A brief account of recent research. Preprint of a paper presented at the Symposium on Science and Technology in the Turkish and Islamic World, Istanbul, June 3–5.
Knorr, W. R., 1989. Textual Studies in Ancient and Medieval Geometry. Birkhäuser, Boston.
——— 1996. The wrong text of Euclid: On Heiberg's text and its alternatives. Centauras 38, 208–276.
Koelblen, S., 1993. Un exercice de combinatoire : Les relations issues de la figure sécante de Ptolémée des six quantités en proportion. Un parcours en histoire des mathématiques : Travaux et recherches, Sciences et Techniques en Perspective, 26, 1–21. Université de Nantes, Nantes.
——— 1994. Une pratique de la composition des raisons dans un exercice de combinatoire. Revue d'histoire des sciences 2, 209–247.
Kunitzsch, P., 1974. Der Almagest: Die Syntaxis Mathematica des Claudius Ptolemäus in arabisch-lateinischer Überlieferung. O. Harrassowitz, Wiesbaden.
Kunitzsch, R, Smart, T, 1986. Short Guide to Modern Star Names and Their Derivations. O. Harrassowitz, Wiesbaden.
Kunitzsch, R, 1989. The Arabs and the Stars: Texts and Traditions on the Fixed Stars, and Their Influence in Medieval Europe. Variorum, Northampton.
——— 1993. Arabische Astronomie im 8. bis 10. Jahrhundert, in [24, pp. 205–220].
Kunitzsch, R, Lorch, R., 1994. Maslama's Notes on Ptolemy's Planisphaerium and Related Texts. Sitzungsberichte der Bayerischen Akademie der Wissenschaften, Philosophisch-historische Klasse, Heft 2.
——— 1993. A note on codex Paris BN ar. 2457. Zeitschrift für Geschichte der arabisch-islamischen Wissenschaften 8, 235–240.
Lorch, R., Kunitzsch, R, 1985. Habash al-Hāsib's Book on the Sphere and Its Use. Zeitschrift für Geschichte der arabisch-islamischen Wissenschaften 2, 68–98.
Lorch, R., 1986. Abū Ja'far al-Khāzin on isoperimetry and the Archimedean tradition. Zeitschrift für Geschichte der arabisch-islamischen Wissenschaften 3, 150–229.
——— 1989. The Arabic transmission of Archimedes' Sphere and Cylinder and Eutocius' Commentary. Zeitschrift für Geschichte der arabisch-islamischen Wissenschaften 5, 94–114.
——— 1994. Mischastrolabien im arabisch-islamischen Kulturgebiet. In: [159, pp. 231–236].
——— 1995. Ptolemy and Maslama on the transformation of circles into circles in stereo graphic projection. Archive for History of Exact Sciences 49, 271–284.
——— 1995. Arabic mathematical sciences: Instruments, texts, transmission. Variorum, Northampton.
——— 1995. Jābir ibn Aflah. and the establishment of trigonometry in the west. Published as No. VIII in [112].
Moreion, R., 1994. Thābit ibn Qurra and Arab astronomy in the 9th century. Arabic Sciences and Philosophy 4, 111–139.
North, J.D., 1994. The Hippopede. In: [159, pp. 143–154].
Plooij, E.B., 1950. Euclid's Conception of Ratio and his Definition of Proportional Magnitudes as Criticized by Arabian Commentators. Ph.D. Thesis, University of Leiden. [Includes the text in facsimile with translation of the commentary on ratio of Abū cAbd Allāh Muhammad ibn Mucādh al-Jayyānī]. |
Ptolemaeus, Claudius, 1986–1991. Der Sternkatalog des Almagest, die arabisch-mittelalterliche Tradition (Kunitzsch, P., hsg. und bearb.), Teil I: Die arabischen Übersetzungen; Teil II: Die lateinische Übersetzung Gerhards von Cremona; Teil III: Gesamtkonkordanz der Sternkoordinaten. O. Harrasowitz, Wiesbaden.
Puig, R., 1985. Concerning the Şafīha Shakkāziyya. Zeitschrift für Geschichte der arabisch-islamischen Wissenschaften 2, 123–139.
——— 1989. Al-Zarqālluh's graphical method for finding lunar distances. Centauras 32,294–309.
Ragep, J., 1993. Naşīr al-Dīn al-Tūsī's Memoir on Astronomy. Springer-Verlag, New York and Berlin.
Rashed, R., 1987. Al-Sijzī et Maimonide : Commentaire mathématique et philosophique de la proposition ii, 14 des Coniques d'Apollonius. Archives internationales d'histoire des sciences 37, 263–296.
——— 1990. A Pioneer in anaclastics: Ibn Sahl on burning mirrors and lenses. Isis 81, 464–491.
——— 1991. Al-Samaw'al, al-Bīrūnī et Brahmagupta : Les méthodes d'interpolation. Arabie Sciences and Philosophy 1, 101–160.
——— 1992. Archimède dans les mathématiques arabes. In: Mueller, I. (ed.), Π?ΡΙ ΤΩN ΜAΘH-ΜAΤΩN. Academic Print Publications, Edmonton, Alberta, pp. 173–193.
——— 1993. Al-Kindī's Commentary on Archimedes' The Measurement of a Circle. Arabic Sciences and Philosophy 3, 7–53.
——— 1993. Géométrie et dioptrique au Xe siècle : Ibn Sahl, al-Qūhī et Ibn al-Haytham. Les Belles Lettres, Paris.
Rebstock, U., 1992. Rechnen im islamischen Orient: die literarischen Spuren der praktischen Rechenkunst. Wissenschaftliche Buchgesellschaft, Darmstadt.
Rosenfeld, B.A., 1988. A History of Non-Euclidean Geometry: Evolution of the Concept of a Geometric Space. Springer-Verlag, New York. Translated from the original Russian edition Istoriya Neevklidovoĭ Geometriĭ. Nauk, Moscow, 1976.
——— 1993. Tashkent manuscripts on mathematical atomism. Studies in the History of Medicine and Science 12, 97–101.
Sabra, A.I., 1987. The appropriation and subsequent naturalization of Greek science in medieval Islam: A preliminary report. History of Science 25, 223–243.
Sabra, A.I., Heinen, A., 1987. On seeing the stars: Edition and translation of Ibn al-Haytham's Risāla fī Ru'yat al-kawākib. Zeitschrift für Geschichte der arabisch-islamischen Wissenschaften 7, 31–72.
Sabra, A.I., 1987. Psychology versus mathematics: Ptolemy and Alhazen on the moon illusion. In: Grant, E., Murdoch, J. (eds.), Mathematics and Its Applications to Science and Natural Philosophy in the Middle Ages: Essays in Honor of Marshall Clagett. Cambridge University Press, Cambridge, pp. 217–247.
——— 1989. The Optics of Ibn al-Haytham, Books I-III: On Direct Vision, 2 Parts. The Warburg Institute, London.
——— 1994. Review of Géométrie et dioptrique au Xe siècle : Ibn Sahl, al-Qūhī et Ibn al-Haytham. Isis 85, 685–686.
——— 1994. Science and philosophy in medieval Islamic theology: The evidence of the fourteenth century. Zeitschrift für Geschichte der arabisch-islamischen Wissenschaften 9, 1–42.
Saliba, G., 1991. The astronomical tradition of Maragha: A historical survey and prospects for future research. Arabic Sciences and Philosophy 1, 67–100.
——— 1994. A History of Arabic Astronomy: Planetary Theories during the Golden Age of Islam. New York University Press, New York. |
Samsó, J., Vernet, J. (eds.), 1992. El legado cientifico andalusí. Museo Arqueológico Nacional, Madrid.
——— 1992. Las ciencias de los antiguos en al-Andalus. Mapire, Madrid.
Samsó, J., Mielgo, H., 1994. Ibn al-Zarqālluh on Mercury. Journal for the History of Astronomy 25, 289–296.
Savage-Smith, E., 1985. Islamicate Celestial Globes: Their History, Construction, and Use. The Smithsonian Institution Press, Washington, DC.
Sesiano, J., 1985. Un système artificiel de numération au moyen ăge. In: Folkerts, M., Lindgren, U. (eds.), Mathemata: Festschrift für Helmuth Gericke. Franz Steiner Verlag Wiesbaden, Stuttgart, pp. 165–196.
——— 1987. Herstellungsverfahren magischer Quadrate aus islamischer Zeit (II). Sudhoffs Archiv 71, 78–87.
——— 1987. Survivance médiévale en Hispanie d'un problème né en Mésopotamie. Centauras 30,18–61.
——— 1987\88. Un complément de Tābit Ibn Qurra au Peri Diaireseon d'Euclide. Zeitschrift für Geschichte der arabisch-islamischen Wissenschaften 4, 149–159.
——— 1991. Un fragment attribué à Archimède. Museum helveticum 48, 21–32.
——— 1991. An Arabie treatise on the construction of bordered magic squares. Historia scien-tiarum 42, 13–31.
——— 1993. Arabische Mathematik im 8.-10. Jahrhundert. In: [24, pp. 399–442].
——— 1994. Quelques méthodes arabes de construction des carrés magiques impairs. Bulletin de la Société vaudoise des sciences naturelles 83, 51–76.
——— 1995. Herstellungsverfahren magischer Quadrate aus islamischer Zeit (III). Sudhoffs Archiv 79, 193–226.
Toomer, G.J. (ed. and trans.), 1990. Apollonius Conies, Books V-VII, The Arabic Translation of the Lost Greek Original in the Version of the Banū Mūsā, 2 vols. Springer-Verlag, New York.
Sharaf al-Dīn al-Tūsī, 1986. Oeuvres mathématiques : Algèbre et géométrie au XIIe siècle. Rashed, R., (ed. and trans.). Les Belles Lettres, Paris.
Vahabzadeh, B., 1994. Two commentaries on Euclid's definition of proportional magnitudes. Arabic Sciences and Philosophy 4, 181–198.
Van Brammelen, G., 1991. The numerical structure of al-Khalīlī's auxiliary tables. Physis 28, 667–687.
——— 1994. A survey of the mathematical tables in Ptolemy's Almagest. In: [159, pp. 155–170].
——— 1994. From drudgery to invention: Astronomical computation in medieval Islam. Proceedings of the Canadian Society for the History and Philosophy of Mathematics 7, 178–189. (Editors: In the original paper, the details of this reference was given as "unpublished manuscript.'' We have provided the published details.)
van Dalen, B., 1993. Ancient and Mediaeval Astronomical Tables: Mathematical Structure and Parameter Values. Ph.D. Dissertation, Universiteit Utrecht.
——— 1994. A table for the true solar longitude in the Jāmic Zīj. In: [159, 171–190].
von Gotstedter, A. (ed.), 1994. Ad Radices: Festband zum fünfzigjährigen Bestehen des Instituts für Geschichte der Naturwissenschaften der Johann Wolfgang Goethe-Universität Frankfürt am Main. Franz Steiner Verlag, Stuttgart.
De Young, G., 1984. The Arabic textual traditions of Euclid's Elements. Historia Mathematica 11, 147–160.
——— 1991. New traces of the lost al-Hajjāj Arabic translations of Euclid's Elements. Physis 38, 647–666.
——— 1992. Abū Sahl's additions to Book II of Euclid's Elements. Zeitschrift für Geschichte der arabisch-islamischen Wissenschaften 7, 73–135.
Young, M.J.L., Latham, J.D., Robert B.S. (eds.), 1990. Religion, Learning and Science in the cAbbasid Period. Cambridge University Press, Cambridge.
Supplementary Bibliography Since submitting the paper we have become aware of other papers relevant to this article which ought to be listed in the bibliography. The size of the bibliography made renumbering impractical so we have listed them here and numbered them consecutively with the last entry of the above bibliography
Berggren, J.L., 1990. Proof and pedagogy in medieval Islamic mathematics. Interchange 2, 36–48. [A special issue titled Creativity, Thought and Mathematical Proof, Hanna, G, Winchester, I. (eds.)]
——— 1994. Historical reflections on scientific knowledge: The case of medieval Islam. In: Hay-hoe, R. (ed.), Knowledge Across Cultures: Universities East and West. OISE Press, Toronto, pp. 137–153.
Berggren, J.L., Thomas, R.S.D., 1996. Euclid's Phaenomena: A Translation and Study of a Hellenistic Treatise in Spherical Astronomy. Garland, New York.
Goldziher, I., 1981. The attitude of orthodox Islam toward the ancient sciences. In: Swartz, M., (trans, and ed.) Studies on Islam. Oxford University Press, New York and Oxford, pp. 185–215.
Hogendijk, J.P., 1988. Three Islamic lunar crescent visibility tables. Journal of the History of Astronomy 19, 29–44.
——— 1994. An Arabic text on the comparison of the five regular polyhedra, "Book XV of the Revision of the Elements by Muhyī al-Dīn al-Maghribī. Zeitschrift für Geschichte der arabisch-islamischen Wissenschaften 8, 133–233.
——— 1995. Mathematics in medieval Islamic Spain. In: Chatterji, S.D., (ed.), Proceedings of the International Congress of Mathematicians, August 3–11, Zurich. Birkhäuser, Basel, vol. 2, pp. 1568–1580.
Muhammad ibn Mūsā al-Khwārizmī, 1992. Le calcul indien (algorismus), André Allard (ed. and trans.). Albert Blanchard, Paris.
Necipoğlu, G, 1995. The Topkapi Scroll: Geometry and Ornament in Islamic Architecture. The Getty Center for the History of Art and the Humanities, Santa Monica, CA.
Sabra, A.I., 1995\6. On seeing the stars, II: Ibn al-Haytham's "answers" to the "doubts" raised by Ibn Macdān. Zeitschrift für Geschichte der arabisch-islamischen Wissenschaften 10, 1–59.
Sesiano, J., 1996. Un traité médiéval sur les carrés magiques : De l'arrangement harmonieux des nombres. Presses polytechniques et universitaires romandes, Lausanne.
Benoĭt, P., Chemia, K., Ritter, J., (eds.), 1992. Histoire de fractions, fractions d'histoire. Birkhäuser, Basel.
Folkerts, M., (ed.), 1996. Mathematische Probleme in Mittelalter: der lateinische und arabische Sprachbereich. Harrassowitz, Wiesbaden.
Ragep, F.J., Ragep, S.P., (eds.), 1996. Tradition, Transmission, Transformation, Proceedings of Two Conferences on Premodern Science Held at the University of Oklahoma. Brill, Leiden and New York.
Kennedy, E.S., 1988. Two medieval approaches to the equation of time. Centauras 31, 1–8.
Samsó, J., 1994. Islamic Astronomy and Medieval Spain. Variorum, Aldershot.
King, DA., 1993. Astronomy in the Service of Islam. Variorum, Aldershot.
Rashed, R., 1991. L'Analyse et la synthèse selon Ibn al-Haytham. In: Rashed, R. (ed.), Mathématiques et philosophie de l'antiquité à l'âge classique : Hommage à Jules Vuillemin. Editions du CNRS, Paris, pp. 131–162.
Berggren, J.L., 1992. Islamic acquisition of the foreign sciences: A cultural perspective. American Journal of Islamic Social Sciences 9, 310–324. Reprinted in [177, 263–284].
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Berggren, J.L. (2014). Mathematics and Her Sisters in Medieval Islam: A Selective Review of Work Done from 1985 to 1995 [1997]. In: Sidoli, N., Van Brummelen, G. (eds) From Alexandria, Through Baghdad. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36736-6_5
Download citation
DOI: https://doi.org/10.1007/978-3-642-36736-6_5
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)