Al‐Karajī

  • Jacques Sesiano
Reference work entry
DOI: https://doi.org/10.1007/978-1-4020-4425-0_9314
Al‐Karajī Abū Bakr Muḥammad was a Persian mathematician and engineer. He held (ca. 1010–1015) an official position in Baghdad during which time he wrote his three main works.
  1. 1.

    His al‐Fakhrīfī'l‐jabr wa ‘l‐muqābala (Glorious on Algebra) contains an exposition of algebra and auxiliary topics (e.g. summing series of integers). The next and larger part is a collection of problems: some are commercial and recreational, but for the most part they belong to indeterminate algebra. All of the latter sorts are taken from Diophantus or Abū Kāmil.

     
  2. 2.

    The Badī˓ fī'l‐ḥisāb (Wonderful on Calculation) is more original. After restating many of Euclid's theorems, al‐Karajī shows how to calculate with square, cubic, and biquadratic roots and with their sums, then how to extract the root of a polynomial in x(this is the earliest known mention of the procedure). A second part contains problems on indeterminate algebra. Here, al‐Karajī has taken the basic methods used by Diophantus in his problems and...

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References

  1. al‐Karajī. Inbāṭ al‐miyāh al‐khafīyah. Hyderabad: Osmania University, 1941.Google Scholar
  2. al‐Karajī. ˓Ilal al‐jabr wa'l‐muqābala. Ankara (Atatürk kültūr merkezi), 1991.Google Scholar
  3. Anbouba, Adel. L'Algèbre al‐Badī  ˓ d'al‐Karagī. Beirut: Université libanaise, 1964.Google Scholar
  4. Hochheim, Adolf. Kâfĩ fĩl ḥisâb (Genügendes über Arithmetik). Halle: Nebert, 1878–1880.Google Scholar
  5. Sesiano, Jacques. Le traitement des équations indéterminées dans le Badī˓ fi'l ḥisāb d'Abū Bakr al‐Karajī. Archive for History of Exact Sciences 17 (1977): 297–379.Google Scholar
  6. Woepcke, Franz. Extrait du Fakhrî. Paris: Duprat, 1853.Google Scholar

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© Springer-Verlag Berlin Heidelberg New York 2008

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  • Jacques Sesiano

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