Ibn Al-Bannā Al Marrākushī

also known as ABŪ’L-‘ABBĀS AHMAD IBN MUḤAMMAD IBN ‘UTHMĀN AL-AZDĪ

(b. Marrakesh, Morocco 29 December 1256; de Marrakesh[?], 1321)

mathematics.

Some authors, following Casiri, say Ibn al-Bannāʾ was a native of Granada. In any case, he studied all the literary and scientific subject that had culutural value in Fez and Marrakesh. Muḥammad ibn yaḥyā al-Sharīf taught him general geometry and Euclid’s Elements; Abū Baker al-Qallūsī nicknamed al Fār (“the Mouse”), introduced him to fractional numbers; and Ibn Ḥajala and Abū ‘Abd Allāh ibn Makhlūf al-Sijimāsī rounded out his training in mathematics. He also studied medicine with al-Mirrīkh, but he did not delve deeply into the subject. The mystic al-Hazmirī was responsible for directing a great part of Ibn al-Bannāʾ’s works to the study of the magic properties of numbers and letters.

He taught arithmetic, algebra, geometry, and astronomy in the madrasa al-ʿAṭṭārīn in Fez. Among his disciples were Abū Zayd ‘Abd al-Rahmān... al-Lajāʾī (d.ca 771/1369) teacher of Ibn Qunfudh, who left us an excellent biographical sketch of Ibn al-Bannnāʾ; muḥammad ibn Ibrāhīm al-Abūli (d 770/1368) Abu’l-Barakāt al-Balāfiqī (d 771/1370), Who had ibn al-Khaṭīb and Ibn Khaldūn as disciples; and Ibn al-Najjār al-Tilimsānī.

H.P.J. Renaud lists eighty-two works by Ibn al-Bannāʾ. The most important scientific ones are an introduction to Euclid; a treatise on areas; an algebra text dedicated to Abū ʿAlī al-Ḥasan al-Milyānī a book about acronical risings and settings (Kitāb al-anwāʾ), which is not as good as his other works on astronomy, such as the Minhāj; and an almanac that is possibly the earliest known, in which the word manākh appears for the first time in its Arabic form. The works of greatest merit, however, are the Talkhīs and the Minhāj.

The Talkhīṣ as its title indicates, is a summary of the lost works of the twelfth- or thirteenth-century mathematician al-Ḥaṣṣār. It was later summarized in verse by Ibn al-Qāḍi (d. 1025/1616) and was often commented on and glossed. Outstanding commentaries are the Rafʿal-ḥijāb by Ibn al-Bannāʾ himself, with notes by Ibn Haydūr and that of al-Qalaṣādī of Granada. These works contain a type of fraction that corresponds to what are today called continuing ascending fractions and an approximate method for extracting square roots that corresponds, more or less, to the third or fourth reduction in the development of the continuous fraction, and is similar to al-Qalaṣādī’s

The possible connection between this formula and that of Juan de Ortega seems evident but the transmission has not been sufficiently proved. The works als contain sums of cubes and squares according to the formulas

1³ + 3³ + 5³ +... + (2n - 1)³ = n²(2n² - 1)

one cannot be sure that Ibn al-Bannāʾ was responsible for introducing a system of mathematical notation.

The Kitāb minhāj al-ṭālib li taʿdīl al-kawākib is a very practical book for calculating astronomical ephemerals, thanks to the attached tables that are based upon those that Ibn Isḥāq al Tūnisī calculated for the year 1222. The theoretical part does not contribute anything new and sometimes gives incorrect relationships between contradictory theories.

Ibn al-Bannāʾ is credited with a Risāla (“epistle”) on the astrolabe called ṣafīḥa shakāziyya a variation of the ṣafīḥa zarqāliyya or “al-Zarqālī’s plate,” which is the topic of many manuscripts in the libraries of north Africa. An examination of some of these manuscripts does scirpts does not show the differences the should, in theory exist between the two instrument.

BIBLIOGRAPHY

I. Original Works. Manuscripts of works by Ibn al-Bannāʾ are listed in Brockelmann, Geschichte der arabischen Litteratur, II (Berlin, 1902), 255, 710; Supp, II (Leiden 1938)363–364; J. Vernet, “Los manuscritos astrómicos de Ibn al-Bannāʾ,” in Actes du VIII Congreès International d’Histoire des Sciences (1956), 297–298; and Griffini in RSO. 7 (1916), 88–106. A. Marre published a French translation of the Talkhīṣ in Atti dell’ Accademia pantificia de Nuovi Linncei, 17 (5 July 1864); the commentary of al-Qalaṣādī was translated by M. F. Woepcke ibid12 (3 April 1859). The Minhāj has been edited, translated into Spanish, and Studied by J. Vernet (Tetuán, 1951). The Kitāb al-anwāʾ was edited, translated into French, and commented on by H.J.P. Renaud (Paris, 1948).

II. Secondary Literature. The Arabic sources for Ibn al-Bannāʾ’s life are listed in al-Ziriklī, al-Aʿlām, 2nd ed., I, 213–214; especially in H. P. J. Renaud, “Ibn al-Bannaʾ de Marrakech ṣūfī et matheématicien,” in Hesperis25 (1938), 13–42 The muqaddima of Ibn khaldūn is fundamental; see the English translation by F. Rosenthal. 3 vols. (New York, 1958) indexes and esp. III, 121, 123, 126, 137. Also consult H. P. J. Renaud, “Sur les dates de la vie du matheématicien arabe marocain Ibn al-Bannāʾ,” in Isis27 (1937), 216–218; “and Sur un passage d’Ibn Khaldoun relatif à l’histoire des mathématiques”in Hesperis31 (1944), 35–47.

Additional information can be found in George Sarton, “Tacuinumk, tawqīm. With a digression on the word ‘Almanac,’” in Isis, 10 (1928), 490–493, and Introduction to the History of Science, II 998–1000; H. suter, Die Mathematiker und Astronomen der Araber under ihre Werke (Leipzig, 1900), 162–164 220, 227; J.A. Sánchez Pérez, Biografias de matemáticos árabes que florecieron en España, no. 44, pp. 51–54; M. Cantor, Vorlesungen ueber Geschichte der Mathematik, I (Leipzig, 197), 805–810; Encyclopedia of Islam, II, 367; M. Steinschneider, “Rectification de quelques erreurs relatives au mathématicien Arabe Ibn al-Banna,” in Bulletino di bibliografia e di storia delle scienze matematiche e fisiche10 (1877), 313; and F. Woepcke, “passages relatifs à des sommations de séries de cubes” in Journal des mathématiques pures et appliquées, 2nd ser., 10 (1865), reviewed by M. Chasles in Comptes rendus des séances de I’Académie des Sciences (27 March 1865).

J. Vernet