Fiqh al-hisab

Ibn Munim al-Abdari divides this work into integers and fractions. Its subject is knowledge of calculation, not a book of rulings, although he connects exposition with purposes of learning arithmetic. The overview names Euclid and part of al-Mutaman's Istikmal as preparatory reading and describes analysis and synthesis in proofs ².

SectionXI of the integer part uses combinations and arrangements in counting words. Models start with ten silk colours and selections of different sizes, then include repeated letters and their markings. A model's twenty-eight letters and maximum length are not a census of every meaningful word or language in use ^{3 4}.

Djebbar identifies inductive and combinatorial construction, not just gathered answers. He compares al-Khalil's linguistic and al-Karaji's algebraic work, questioning absence of a connection between the triangle and binomial coefficients in root extraction. Modern notation permitting that connection does not let us complete a historical claim on the author's behalf. Scholarly explanation and original wording are different layers ⁵.

Djebbar reports a practical section and tables added after copies circulated among students. A surviving version need not be a single composition layer produced on a known day. Prefatory praise of al-Nasir suggests1207–1212 to the historian, not a dated scribal ending. Reported praise of Ibn Tumart is authorial rhetoric, not museum endorsement ⁶.

Arrabita describes a copy in collection416, pages214–419, written by Hasan al-Rabai in Tunis958AH/1551. It reports Idriss Lamrabet's1981 discovery and2005 Dar al-Aman edition in Rabat. These are article details, not our inspection of manuscript or edition; copying year does not date invention of the combinatorial procedures ⁷.

A sole-known-copy statement in the edition's context is not our survey of all present libraries. Modern symbolic translations added by the editor to explain verbal problems are not automatically the author's writing. Changing prose into Latin symbols does not date its reasoning to modern times either; each layer needs attribution ⁸.

We read the institutional overview and selected Djebbar printed5–13,19–23, visually inspecting19–20. We did not read the entire book, the study's reproduced Arabic section or the2005 edition. A downloadable study is not firsthand manuscript reading. Source files and OCR stay outside Git. Modern museum examples check selection rules, not a claimed literal transcription of original table cells ⁹.