Abū Kāmil. Algèbre et analyse Diophantienne. Édition, traduction et commentaire
Bibliographic record
Abstract
After al-Khwārizmī, Abū Kāmil (late ninth century) is the next Arabic author whose book on algebra is extant in its entirety.Where al-Khwārizmī's book was deliberately brief, Abū Kāmil's Kitāb al-jabr wa'l-muqābala (Book of Algebra) occupies 111 folios in the only surviving manuscript. 1 That is long enough for Abū Kāmil to show features and techniques omitted by al-Khwārizmī and to exhibit his own originality with regard to proofs, irrational numbers, and the manipulation of algebraic expressions.Abū Kāmil's influence was deservedly almost as far-reaching as al-Khwārizmī's.The Book of Algebra became a major influence on such well-known figures as al-Karajī, al-Samawʾal, and Ibn al-Bannāʾ, as well as on lesser ones like ʿAlī al-Sulamī and Ibn Badr.Most of the book was translated into Latin in the 12th century and whole portions found their way into the Liber Mahameleth in the 12th century, into Fibonacci's Liber abaci and De practica geometrie in the 13th century, and into Jean de Murs' Liber quadripartitum in the 14th century.From there its influence spread through Italian abbacus texts to Luca Pacioli's Summa de arithmetica of 1494 and into 16th-century European algebra.We also possess several manuscripts of a Hebrew translation made before 1475, possibly in Spain. 2 Two other books of Abū Kāmil are extant.One is his brief Kitāb al-Ṭayr (Book of Birds), in which he uses algebra to solve problems with several ⋆ English translations are mine unless noted otherwise.In referring to Rashed's text, '579.13',e.g., means 'page 579, line 13'. 1 Istanbul, Beyazit Library, Kara Muṣṭafā Paşa 379 (now 19046).Copied in AD 1253.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.003 | 0.003 |
| Science and technology studies | 0.003 | 0.003 |
| Scholarly communication | 0.006 | 0.004 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.004 |
| Insufficient payload (model declined to judge) | 0.038 | 0.021 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".