8vo. 200 pp., of German, 336 pp., of Arabic text, figures, 5 pages scanned from original manuscripts, biblio, original wrappers, title in Arabic and English, copy in Mint condition, Aleppo University, Institute for the History of Arabic Science, Aleppo, 2004.

Synopsis

There is certainly no doubt that Abu Kamil considered that he was building on the foundations of algebra as set up by al-Khwarizmi and indeed he forms an important link in the development of algebra between al-Khwarizmi and al-Karaji. There is another reason for Abu Kamil’s importance, however, which is that his work was the basis of Fibonacci’s books. So not only is Abu Kamil important in the development of Arabic algebra, but, through Fibonacci, he is also of fundamental importance in the introduction of algebra into Europe. The author of presents a list of parallels between Abu Kamil’s works on algebra and the works of Fibonacci, and he also discusses the influence of Abu Kamil on two algebra texts of al-Karaji.
The Book on algebra by Abu Kamil is in three parts: (i) On the solution of quadratic equations, (ii) On applications of algebra to the regular pentagon and decagon, and (iii) On Diophantine equations and problems of recreational mathematics. The part on the regular pentagon and decagon is studied in detail in, while the remainder of the work is described in the content of the work is the application of algebra to geometrical problems. It is the combination of the geometric methods developed by the Greeks together with the practical methods developed by al-Khwarizmi mixed with Babylonian methods.