Research Article
BibTex RIS Cite

Hârezmî, Ibn Türk, ve Liber Mensurationum : İslâm Cebirinin Kökenleri Üzerine

Year 1986, Volume: 2 Issue: 5, 445 - 484, 01.05.1986

Abstract

References

  • Anbouba, A del, 1978. “ Acquisition de l ’algebre par les Arabes et premiers developpements. A perçu general” , Journal for the History o f Arabic Science 2, 66-100.
  • Baillet, J ., 1892. “ L e papyrus m athem atique d ’A khm îm ” , Mission Archeologique Française au Caire, Memoires g : 1 (Paris), 1-89.
  • Baqir, Taha, 1951. “ Some More Mathematical Texts from Teli Harmal” , Sümer 7, 28-45.
  • Bergh, Paul, 1886. “ Seiten - und D iam etralzahlen bei den G riechen” , Zeitschrift für Mathematik und Physik. Historisch - literarische Abtheilung 31, 135.
  • Boncompagni, Baldassare, 1851. “ D ella vita e delle öpere di G herardo cremonese, traduttore del secolo duodecim o, e di G herardo da Sabionetta astronomo del secolo decim oterzo” , Atti delVAccademia pontificia de’ Nuovi Lincei 4. (1850-51), 387-493-
  • ,Boncom pagni, Baldassare, ed., 1862. Şeritti di Leonardo Pisano. II. Leonardi Pisani Practica geometriae ed Opusculi, R om a: T ip o grafia delle Scienze M atem atiche e Fisiche.
  • Busard, H .L .L ., 1968. “ L ’algebre au moyen âge: Le ‘Liber m ensurationum’ d ’A bû Bekr” , Journal des Savants, Avril-Juin 1968, 65-125.
  • Busard, H .L .L ., ed., 1983. The First Latin Translation of Emlide Elements Commonly Ascribed to Adelard of Bath. (Studies and Texts, 64). Toronto : Pontifical Institute o f M edieval Studies.
  • Cantor, M oritz, 1875. Die römisehe Agrimensoren und ihre Stellung in der Geschichte der Feldmesskunst. L eipzig: Teubner, 1875.
  • Glagett, M arshall, 1984. Archimedes in the Middle Ages. V . Quas Archimedean Geometry in the Thirteenth Century. (M emoirs of the Am ericanPhilosophical Society, 157 A + B ) . Philadelphia : T h e Am erican philosophical Society.
  • [Colebrooke, H .T .] 1817. Algebra, with Arithmetic and Mensuration from the Sanscrit o f Brahmegupta and Bhascara, Translated by H enry Thom as Colebrooke. London: John M urray. R eprint YViesbaden: M artin Sândig, 1973.
  • Curtze, M axim ilian, ed., 1902. Urkunden zur Geschichte der Mathematik im Mittelalter und der Renaissance. (Abhandlungen zur Geschichte der mathematisehen Wissensehaften, 12-13). L eipzig: Teubner.
  • D atta, Dibhutibhusan, — Avadhesh N arayan Singh, 1962. History o f Hindu Mathematics. A Source Book. Parts I and II. B om bay: A sia Publishing House. Reprint in one volüme o f the first edition, Lahore 1935-38.
  • Folkerts, Menso, 1970. “ Boethius” Geometrie II. Einmathematisehes Lehrbuch des Mittelalters. Wiesbaden: Franz Steiner.
  • Folkerts, M ., 1978. “ D ie alteste mathematisehe Aufgabensam m lung in lateiniseher Sprache: Die A lkuin zugeschriebenen Propositines ad acuendos iuverıes. Ü berlieferung, Inhalt, kritisehe Edition” . Österreichische Akademie der Wissenschaften, Mathematisch - Naturwissenschaftliche Klasse. Denkschriften, 116. Band, 6. A bhandlung. G andz, Solom on, 1926. “ The Origin o f the Term ‘Algebra’ ” . American Mathematical Monthly 33, 437*44‘o

Al-Khwârizmî, Ibn Turk, and the Liber Mensurationum : On the Origins of Islamic Algebr

Year 1986, Volume: 2 Issue: 5, 445 - 484, 01.05.1986

Abstract

A close investigation o f O ld Babylonian second-degree algebra shows that its method and conceptualization are not arithm etical and rhetorical, as is grosso modo the al-jabr presented by A l-K hw ârizm î. Instead, it appears to be based on a “ naive” geom etry o f areas very similar to that used by lbn T urk and A l-K hw ârizm î in their justifications o f the algorithms used in al-jabr to solve the basic mixed second-degree equations. This raises in a new light the question whether the early Islam ic use o f geometric justifications was a graft o f Greek methods
upon a “ sub-scientific” m athem atical tradition, as often maintained, or the relation o f early Islam ic algebra to its sources must be seen differently.

References

  • Anbouba, A del, 1978. “ Acquisition de l ’algebre par les Arabes et premiers developpements. A perçu general” , Journal for the History o f Arabic Science 2, 66-100.
  • Baillet, J ., 1892. “ L e papyrus m athem atique d ’A khm îm ” , Mission Archeologique Française au Caire, Memoires g : 1 (Paris), 1-89.
  • Baqir, Taha, 1951. “ Some More Mathematical Texts from Teli Harmal” , Sümer 7, 28-45.
  • Bergh, Paul, 1886. “ Seiten - und D iam etralzahlen bei den G riechen” , Zeitschrift für Mathematik und Physik. Historisch - literarische Abtheilung 31, 135.
  • Boncompagni, Baldassare, 1851. “ D ella vita e delle öpere di G herardo cremonese, traduttore del secolo duodecim o, e di G herardo da Sabionetta astronomo del secolo decim oterzo” , Atti delVAccademia pontificia de’ Nuovi Lincei 4. (1850-51), 387-493-
  • ,Boncom pagni, Baldassare, ed., 1862. Şeritti di Leonardo Pisano. II. Leonardi Pisani Practica geometriae ed Opusculi, R om a: T ip o grafia delle Scienze M atem atiche e Fisiche.
  • Busard, H .L .L ., 1968. “ L ’algebre au moyen âge: Le ‘Liber m ensurationum’ d ’A bû Bekr” , Journal des Savants, Avril-Juin 1968, 65-125.
  • Busard, H .L .L ., ed., 1983. The First Latin Translation of Emlide Elements Commonly Ascribed to Adelard of Bath. (Studies and Texts, 64). Toronto : Pontifical Institute o f M edieval Studies.
  • Cantor, M oritz, 1875. Die römisehe Agrimensoren und ihre Stellung in der Geschichte der Feldmesskunst. L eipzig: Teubner, 1875.
  • Glagett, M arshall, 1984. Archimedes in the Middle Ages. V . Quas Archimedean Geometry in the Thirteenth Century. (M emoirs of the Am ericanPhilosophical Society, 157 A + B ) . Philadelphia : T h e Am erican philosophical Society.
  • [Colebrooke, H .T .] 1817. Algebra, with Arithmetic and Mensuration from the Sanscrit o f Brahmegupta and Bhascara, Translated by H enry Thom as Colebrooke. London: John M urray. R eprint YViesbaden: M artin Sândig, 1973.
  • Curtze, M axim ilian, ed., 1902. Urkunden zur Geschichte der Mathematik im Mittelalter und der Renaissance. (Abhandlungen zur Geschichte der mathematisehen Wissensehaften, 12-13). L eipzig: Teubner.
  • D atta, Dibhutibhusan, — Avadhesh N arayan Singh, 1962. History o f Hindu Mathematics. A Source Book. Parts I and II. B om bay: A sia Publishing House. Reprint in one volüme o f the first edition, Lahore 1935-38.
  • Folkerts, Menso, 1970. “ Boethius” Geometrie II. Einmathematisehes Lehrbuch des Mittelalters. Wiesbaden: Franz Steiner.
  • Folkerts, M ., 1978. “ D ie alteste mathematisehe Aufgabensam m lung in lateiniseher Sprache: Die A lkuin zugeschriebenen Propositines ad acuendos iuverıes. Ü berlieferung, Inhalt, kritisehe Edition” . Österreichische Akademie der Wissenschaften, Mathematisch - Naturwissenschaftliche Klasse. Denkschriften, 116. Band, 6. A bhandlung. G andz, Solom on, 1926. “ The Origin o f the Term ‘Algebra’ ” . American Mathematical Monthly 33, 437*44‘o
There are 15 citations in total.

Details

Primary Language English
Journal Section Erdem
Authors

Jens Hoyrup This is me

Publication Date May 1, 1986
Published in Issue Year 1986 Volume: 2 Issue: 5

Cite

APA Hoyrup, J. (1986). Al-Khwârizmî, Ibn Turk, and the Liber Mensurationum : On the Origins of Islamic Algebr. Erdem, 2(5), 445-484.

ERDEM Journal is indexed by TR Dizin, MLA International Bibliography, EBSCOhost, SOBIAD, ASI (Advanced Science Index) ISAM, DAVET and AYK Journal Index.