Lost Greek Mathematical Works in Arabic Translation

  • G. J. Toomer
Part of the Boston Studies in the Philosophy of Science book series (BSPS, volume 240)


The works of the ancient Greek mathematicians which we possess represent only a few fragments from the wreck of the great treasure ship of Hellenistic mathematics. What has come down to us is little more than a reflection of the pedagogical interests of the schoolmen of late antiquity and Byzantine times, who caused to be copied only those works which were of some use in the curricula of their institutions of higher education at Alexandria, Antioch, Athens, Constantinople, and a very few other places. Their choice illustrates the impoverished intellectual climate of the Greek world in the millennium from the third to the thirteenth century a.d. Thus the compendium of elementary geometry which goes under the name of Euclid was transmitted through the schoolrooms, but none of the works on higher geometry which Euclid wrote (probably in the early third century b.c.) has been preserved; and only the first four books of Apollonius’ Conics, which treat the elements of the theory, continued to be copied in Byzantine times: The last four books, which deal with more advanced topics, are lost in Greek.


Ninth Century Mathematical Work Arabic Text Late Antiquity Latin Translation 
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  1. 1.
    The Arabic translation has been lost in its turn, but for a bad Latin translation made from the Arabic in the twelfth century, see A. Lejeune, ed. (1956) LOptique de Claude Ptolémée, LouvainGoogle Scholar
  2. 2.
    Apollonii Pergaei Conicorum libri octo et Sereni Antissensis de sectione cylindri et coni libri duo (1710) OxfordGoogle Scholar
  3. 3.
    Apollonii Pergaei de sectione rationis libri duo (1706) OxfordGoogle Scholar
  4. 4.
    William Thomson and Gustav Junge, eds. (1930) The Commentary of Pappus on Book X of Euclids Elements, Cambridge, Mass.Google Scholar
  5. 5.
    J. Wurschmidt (1925) Die Schrift des Menelaus über die Bestimmung der Zusammensetzung von Legierungen, Philologus 80: 377–409. Wurschmidt gives only a German translation. The Arabic text has never been printedGoogle Scholar
  6. 6.
    Hellmut Ritter (1953) Autographs in Turkish Libraries, Oriens 6: 63CrossRefGoogle Scholar
  7. 7.
    Max Krause (1936) Stambuler Handschriften islamischer Mathematiker, Quellen Stud. Gesch. Math. Astron. Phys. B3: 437–532Google Scholar
  8. 8.
    Fuat Sezgin (1967–) Geschichte des Arabischen Schrifttums, Leiden (eight volumes published to date)Google Scholar
  9. 9.
    G. J. Toomer, ed. and trans. (1976) Diocles on Burning Mirrors, Sources in the History of Mathematics and Physical Sciences 1, Berlin-Heidelberg-New YorkGoogle Scholar
  10. 10.
    Jacques Sesiano, ed. and trans. (1982) Book IV to VII ofDiophantusArithmetica in the Arabic Translation Attributed to Qustâ ibn Lûqa¯, Sources in the History of Mathematics and Physical Sciences 3, New York-Heidelberg-BerlinGoogle Scholar
  11. 1.
    The work will be published, with a translation, by D. E. P. Jackson in Sources in the History of Mathematics and Physical Sciences. See provisionally D. E. P. Jackson (1980) Towards a Resolution of the Problem of râ âvi Staar† µart ypatpdµeva in Pappus’ Collection Book VIII,” Classical Q. 30: 523–533Google Scholar
  12. 12.
    On the history of the problem see W. M. Kutta (1897) Zur Geschichte der Geometrie mit constanter Zirkelöffnung, Nova Acta Leopoldina 81:71–101. Kutta, however, could not have known either of Mohr or of the Arabic PappusGoogle Scholar
  13. 13.
    J. Hogendijk, ed. and trans. (1983) ( Doctoral thesis, Utrecht), to be published in Sources in the History of Mathematics and Physical SciencesGoogle Scholar
  14. 14.
    Published so far: The Optics of ibn al-Haytham (1983) Books I–III, the Arabic text, KuwaitGoogle Scholar

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© Springer Science+Business Media Dordrecht 2004

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  • G. J. Toomer

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