Abu Kamil

Abu Kamil (Arabic: ابو كامل), whose full name is Abu Kamil Schuja ibn Aslam ibn Muhammad ibn Schuja , was an Arabic mathematician . He lived from around 850 to 930 AD and probably came from Egypt ; no further biographical information is known. He was called al-Hasib al-Misri , "the Egyptian calculator".

Root terms

He found general relationships between root expressions , which are found in the following equations, among others, which he established and confirmed with the aid of binomial formulas .

${\displaystyle {\sqrt {18}}+{\sqrt {8}}={\sqrt {50}}}$

or

${\displaystyle {\sqrt {18}}-{\sqrt {8}}={\sqrt {2}}}$

algebra

Abu Kamil wrote several mathematical works. In his algebra ( Al-Kitab al-jabr wa'l-muqabala ) he continued the algebra of al-Khwarizmis . The book comprises 111 folio pages in the only surviving Arabic version from the 13th century, which is now kept in Istanbul (MS 379 [19046] of the Kara Muṣṭafā Paşa collection in the Beyazit library). Latin and a Hebrew translation established the lasting effect of this script. The algebra was used by Fibonacci and al-Karaji .

Other works

“The Book of Rarities in Arithmetic” contains six different tasks that lead to linear systems of equations and require whole-number or fractional solutions, so-called bird problems.

A work on land surveying by Abu Kamil is also preserved. Other mathematical works are known by their title, but not preserved.

expenditure

• Sami Chalhoub: The Algebra: Kitab al-Gabr wal-muqabala of Abu Kamil Soga ibn Aslam . Aleppo, 2004.
• Martin Levey: The algebra of Abū Kāmil: Kitāb fī al-Jabr wa'l-muqābala / in a commentary by Mordecai Finzi (Hebrew with English translation), Madison: University of Wisconsin Press, 1966.
• LC Karpinski: The book of rarities in arithmetic by Abu Kamil al Misri , (German translation) in: Bibl. Math. 12 (1911) / 12 pp. 40-55.
• Roshdi Rashed: Abu Kamil: Algèbre et analyze diophantienne. Edition, traduction, commentaire historique et mathématique . Berlin: De Gruyter 2012.
• Jacques Sesiano: Abū Kāmil's Book on Mensuration , in: N. Sidoli and G. Van Brummelen (eds.), From Alexandria, Through Baghdad, Surveys and Studies in the Ancient Greek and Medieval Islamic Mathematical Sciences in Honor of JL Berggren, Heidelberg: Springer Verlag, 2014, pp. 359–408.
• Joseph Weinberg: The algebra of Abu Kāmil Soga ben Aslam , dissertation in Munich at the Philosophical II section, Munich, 1935.. .

Web links

• John J. O'Connor, Edmund F. Robertson :  Abu Kamil. In: MacTutor History of Mathematics archive .
• Biography of the Swiss Federal Institute of Technology in Zurich

Individual evidence

1. ↑ On the meaning of this work: “The algebra of ABO KAMIL SHUJA '(c. 900) [..] is now available in a German translation made by DR. JOSEF WEINBERG from the Hebrew version of MORDECAI FINZI (c. I470). ABO KAMIL's work is of great importance for the history of algebra and deserves further investigation. ABO KAMIL SHUJA had deeply influenced LEONARDO FIBONACCI (c. I2oo) and through him mediaeval mathematics in general. He is the first known to us to relate Oriental algebra to Greek geometry, by referring to EUCLID, II 5-6, as furnishing the demonstration for the solution of the quadratic equations. "( Geschichte der Elementar-Mathematik by Johannes Tropfke ( Memento des Originals from July 14, 2018 in the Internet Archive ) Info: The archive link has been inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice. )