Abū Kāmil. Algèbre et analyse Diophantienne. Édition, traduction et commentaire
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Bibliographic record
Abstract
After al-Khwrizm, Ab Kmil (late ninth century) is the next Arabic author whose book on algebra is extant in its entirety. Where al-Khwrizm's book was deliberately brief, Ab Kmil's Kitb al-jabr wa'l-muqbala (Book of Algebra) occupies 111 folios in the only surviving manuscript. 1 That is long enough for Ab Kmil to show features and techniques omitted by al-Khwrizm and to exhibit his own originality with regard to proofs, irrational numbers, and the manipulation of algebraic expressions. Ab Kmil's influence was deservedly almost as far-reaching as al-Khwrizm's. The Book of Algebra became a major influence on such well-known figures as al-Karaj, al-Samawal, and Ibn al-Bann, as well as on lesser ones like Al al-Sulam 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 Ab Kmil are extant. One is his brief Kitb al-ayr (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 Muaf Paa 379 (now 19046). Copied in AD 1253.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.015 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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 it