مخطوطة بخشالي

الأرقام المستخدمة في مخطوطة بخشالي

مخطوطة بخشالي Bakhshali manuscript هي مخطوطة رياضية مكتوبة على لحاء البتيولا عـُثر عليها بالقرب من قرية بخشالي (بالقرب من مردان في پاكستان الحالية) في 1881. وترجع أهميتها لكونها أقدم مخطوطة موجودة في الرياضيات الهندية."[1] أجزاء منها تم تسنينها إلى 224–383 م.

وهي أقدم دليل على استخدام الهنود لرمز صفر.[2][3]

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

الاكتشاف

المخطوط عثر عليه في 1881،[4] فلاح في قرية بخشالي، الواقعة بالقرب من مردان، في خيبر پختون‌خوا، پاكستان.[1] البحث الأولي في المخطوط قام به أ. ف. ر. هورنليه.[1][5] بعد وفاة هورنليه، فحصها G. R. Kaye، الذي حرر الدراسة ونشرها ككتاب في 1927.[6]

المخطوطة المتواجدة هي غير كاملة، وتتكون من سبعين ورقة من لحاء البتيولا,[1][4] ولا يُعرف الغرض منها.[1] وتوجد حالياً في مكتبة بودليان في جامعة أكسفورد[1][4] (MS. Sansk. d. 14)، ويقال أنها هشة بشكل لا يسمح بفحصها من قبل الدارسين.


المحتويات

The manuscript is a compendium of rules and illustrative examples. Each example is stated as a problem, the solution is described, and it is verified that the problem has been solved. The sample problems are in verse and the commentary is in prose associated with calculations. المسائل تتضمن الحساب والجبر والهندسة, including mensuration. المواضيع المغطاة تتضمن الكسور والجذور التربيعية والمتتاليات الحسابية والهندسية، solutions of simple equations, المعادلات الخطية الآنية والمعادلات التربيعية وindeterminate equations of the second degree.[6][7]

The manuscript is written in an earlier form of Śāradā script, which was mainly in use from the 8th to the 12th century، في الجزء الشمالي الغربي من الهند، مثل كشمير والمناطق المجاورة.[1] The language is the Gatha dialect (which is a combination of اللغات الهندية القديمة السنسكريتية وPrakrit).

A colophon to one of the sections states that it was written by a brahmin identified as "the son of Chajaka", a "king of calculators," for the use of Vasiṣṭha's son Hasika. The brahmin might have been the author of the commentary as well as the scribe of the manuscript.[7] Near the colophone appears a broken word rtikāvati, which has been interpreted as the place Mārtikāvata mentioned by Varāhamihira as being in northwestern India (along with Takṣaśilā, Gandhāra etc.), the supposed place where the manuscript might have been written.[1]

الرياضيات

The manuscript is a compilation of mathematical rules and examples (in verse), and prose commentaries on these verses.[1] Typically, a rule is given, with one or more examples, where each example is followed by a "statement" (nyāsa / sthāpanā) of the example's numerical information in tabular form, then a computation that works out the example by following the rule step-by-step while quoting it, and finally a verification to confirm that the solution satisfies the problem.[1] This is a style similar to that of Bhāskara I's commentary on the gaṇita (mathematics) chapter of the Āryabhaṭīya, including the emphasis on verification that became obsolete in later works.[1]

The rules are algorithms and techniques for a variety of problems, such as systems of linear equations, quadratic equations, arithmetic progressions and arithmetico-geometric series, computing square roots approximately, dealing with negative numbers (profit and loss), measurement such as of the fineness of gold, etc.[4]

تأريخ

في 2017, three samples from the manuscript were shown by radiocarbon dating to come from three different centuries: from AD 224–383, 680–779, and 885–993. It is not known how fragments from different centuries came to be packaged together.[8][9][10]

Prior to this finding, most scholars agreed that the physical manuscript was a copy of a more ancient text, whose date had to be estimated based on content. Hoernle thought that the manuscript was from the 9th century, but the original was from the 3rd or 4th century.[أ] Indian scholars assigned it an earlier date. Datta assigned it to the "early centuries of the Christian era."[6] Channabasappa dated it to AD 200–400, on the grounds that it uses mathematical terminology different from that of Aryabhata.[12] Hayashi stated that it was from no later than the 7th century.[13]

الأرقام والصفر

The Bakshali manuscript uses numerals with a place-value system, using a dot as a place holder for zero.[14] The dot symbol came to be called the shunya-bindu (literally, the dot of the empty place). References to the concept are found in Subandhu's Vasavadatta, which has been dated between 385 and 465 CE by the scholar Maan Singh.[15]

Prior to the 2017 carbon dating, a 9th-century inscription of zero on the wall of a temple on the grounds of Gwalior Fort[16] in Gwalior, Madhya Pradesh, was thought to be the oldest Indian use of a zero symbol.[17]

انظر أيضاً

ملاحظات

  1. ^ G. R. Kaye, on the other hand, thought in 1927 that the work was composed in the 12th century,[1][6] but this was discounted in recent scholarship. G. G. Joseph wrote, "It is particularly unfortunate that Kaye is still quoted as an authority on Indian mathematics."[11]

المراجع

  1. ^ أ ب ت ث ج ح خ د ذ ر ز س Takao Hayashi (2008), "Bakhshālī Manuscript", in Helaine Selin, Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures, 1, Springer, pp. B1-B3, ISBN 9781402045592, https://books.google.com/books?id=kt9DIY1g9HYC&lpg=RA1-PA1&pg=RA1-PA1 
  2. ^ Devlin, Hannah (2017-09-13). "Much ado about nothing: ancient Indian text contains earliest zero symbol". The Guardian. ISSN 0261-3077. Retrieved 2017-09-14.
  3. ^ "Carbon dating finds Bakhshali manuscript contains oldest recorded origins of the symbol 'zero'". Bodleian Library. 2017-09-14. Retrieved 2017-09-14.
  4. ^ أ ب ت ث John Newsome Crossley; Anthony Wah-Cheung Lun; Kangshen Shen; Shen Kangsheng (1999). The Nine Chapters on the Mathematical Art: Companion and Commentary. Oxford University Press. ISBN 0-19-853936-3.
  5. ^ Hoernle, Augustus (1887), On the Bakshali manuscript, Vienna: Alfred Hölder (Editor of the Court and of the University), https://archive.org/details/onbakshalimanusc00hoeruoft 
  6. ^ أ ب ت ث Bibhutibhusan Datta (1929). "Book Review: G. R. Kaye, The Bakhshâlî Manuscript—A Study in Mediaeval Mathematics, 1927". 35 (4). Bull. Amer. Math. Soc.: 579–580. {{cite journal}}: Cite journal requires |journal= (help)
  7. ^ أ ب Plofker, Kim (2009), Mathematics in India, Princeton University Pres, ISBN 978-0-691-12067-6 
  8. ^ Devlin, Hannah (2017-09-13). "Much ado about nothing: ancient Indian text contains earliest zero symbol". The Guardian. ISSN 0261-3077. Retrieved 2017-09-14.
  9. ^ Mason, Robyn (2017-09-14). "Oxford Radiocarbon Accelerator Unit dates the world's oldest recorded origin of the zero symbol". School of Archaeology, University of Oxford. Retrieved 2017-09-14.
  10. ^ "Carbon dating finds Bakhshali manuscript contains oldest recorded origins of the symbol 'zero'". Bodleian Library. 2017-09-14. Retrieved 2017-09-14.
  11. ^ Joseph, G. G. (2000), The Crest of the Peacock, non-European roots of Mathematics, Princeton University Press 
  12. ^ E. F. Robinson (May 2002). "The Bakhshali manuscript". The MacTutor History of Mathematics archive. Archived from the original on 9 August 2007. Retrieved 2007-07-24. {{cite web}}: Unknown parameter |deadurl= ignored (|url-status= suggested) (help)
  13. ^ T Hayashi, The Bakhshali manuscript: An ancient Indian mathematical treatise (Groningen, 1995).
  14. ^ Pearce, Ian (May 2002). "The Bakhshali manuscript". The MacTutor History of Mathematics archive. Retrieved 2007-07-24.
  15. ^ Singh, Maan (1993). Subandhu, New Delhi: Sahitya Akademi, ISBN 81-7201-509-7, pp. 9–11.
  16. ^ Joseph, George Gheverghese (26 Jul 2016). Indian Mathematics: Engaging with the World from Ancient to Modern Times. World Scientific. ISBN 1786340631. In a temple on the path up to Gwalior Fort [...] where we find a circular zero in the terminal position. {{cite book}}: |access-date= requires |url= (help)
  17. ^ "Carbon dating finds Bakhshali manuscript contains oldest recorded origins of the symbol 'zero'". Bodleian Library. 2017-09-14. Retrieved 2017-09-14.

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