Abu Kamil's Book of Algebra

Abu Kamil Shuja ibn Aslam's Book of Algebra is distinct from al-Khwarizmi's similarly titled work. Scholarship attributes expanded algebraic computation to it, especially irrational coefficients as well as solutions, connecting earlier algebra with Euclidean geometry ^{1 2}.

MacTutor describes three parts: quadratic equations, algebra applied to regular pentagons and decagons, and indeterminate and recreational problems. It reports69 problems, including problems known from al-Khwarizmi but approached differently. This is the biography's count, not our own manuscript census ².

TDV distinguishes an irrational solution from an irrational coefficient. This underlies the particular contribution linked to the work; not every section becomes one invention. It also describes unknowns, higher powers and operations with radicals, noting separate works on transactions and bequests rather than treating those applications as the whole algebra ¹.

MacTutor explains the verbal naming of powers and the use of powers beyond what we now writex². Contemporary symbols therefore do not document the author's handwriting. TDV emphasizes geometric explanation and Euclidean foundations, multiple solutions and an approach extending beyond mechanically repeating one procedure ^{3 1}.

Dosay's modern exposition includes dividing ten and radical problems. We read pp57–60,66–68 and inspected the image ofp66 to verify a product containing square roots of3 and2. This is neither a reading of the whole article/book nor a claim that Dosay's symbols photograph the author's manuscript ⁴.

TDV reports two Arabic witnesses, complete at Beyazit and incomplete at Mashhad, and Fuat Sezgin's1986 facsimile. It also describes a Hebrew version apparently incomplete relative to Arabic and a Latin translation containing only the first two parts. These are the entry's reports, not the result of our inspection of those copies ¹.

The entry names old commentaries without identifying them as surviving, attributes praise to Ibn Khaldun and discusses al-Karaji and Fibonacci's reception. Existence of a translation, survival of a complete text and transmission of a particular problem remain different questions. General reception does not establish that every modern technology depends on this work ^{5 6}.

Personal information is scarce and MacTutor's dates approximate; an exact composition date is therefore not added without evidence. The author's activity, copying and modern publication cannot be collapsed. Neither the Arabic original nor old translations were read here. Direct evidence consists of specified studies; the older Cairo-introduction source remains preserved in the maker record ^{7 8}.

Readers can check our modern examples independently, but a correct symbolic expansion does not replace a critical edition. This limit belongs to an honest description, without diminishing the refinement scholarship attributes to the book.