Al-Samawal's al-Bahir in algebra

Al-Bahir in algebra is al-Samawal al-Maghribi's work, described by biographies as composed at nineteen with possible later revisions; no exact composition year is calculated from that age and approximate biographical dates ^{1 2}. It preserves information about lost work of Karaji while presenting broader algebraic operations and calculations ¹.

The first treats premises, multiplication, division and root extraction; the second unknown quantities, equations and summations; the third irrational magnitudes; and the fourth problem classification ¹. The biography describes negative quantities and polynomial operations alongside geometrical demonstrations for quadratic equations, so arithmetic development does not mean the abolition of all geometry ¹. The irrational-magnitudes section follows Euclid's tenth book, while problem classification distinguishes solvable cases, cases not known to be solvable, and cases whose assumed solution leads to contradiction ¹.

The second part preserves binomial-coefficient calculation attributed to Karaji; the biographies describe it as the surviving account of a lost original computation ^{1 2}. The work's relation to that record is consequently “describes,” not “first describes” or “Karaji's autograph” ¹. MacTutor's reproduced translation is a modern intermediary, not an independent Arabic reading undertaken for this page ³.

The biography places youthful composition before al-Samawal's1163 conversion to Islam, while Anbouba allows subsequent revisions; neither fixes every surviving passage's date ^{1 2}. No blanket claim that the entire book was composed during his Islamic period, or an unsupported personal religious school, is added.

Anbouba's bibliography lists Istanbul witnesses Aya Sofya2718 and Esat Efendi3155 and an Ahmad/Rashed edition at Damascus, giving1972 in one place and1971 elsewhere in the same entry ⁴. Images, current catalogues and that edition were not inspected here, and no modern page numbers are presented as pages we read. Anbouba calls the work's influence difficult to assess, suggests indirect restricted influence on al-Kashi, and describes it as apparently unknown in the West ². This is his attributed assessment, not a universal museum verdict.

MacTutor, Dictionary of Scientific Biography and Karaji biography ^{1 2 4 3}.