Ibn Al-Bann? Al Marr?kush?

also known as AB?’L-‘ABB?S AHMAD IBN MU?AMMAD IBN ‘UTHM?N AL-AZD?

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

mathematics.

Some authors, following Casiri, say Ibn al-Bann?? was a native of Granada. In any case, he studied all the literary and scientific subject that had culutural value in Fez and Marrakesh. Mu?ammad ibn ya?y? al-Shar?f taught him general geometry and Euclid’s Elements; Ab? Baker al-Qall?s? nicknamed al F?r (“the Mouse”), introduced him to fractional numbers; and Ibn ?ajala and Ab? ‘Abd All?h ibn Makhl?f al-Sijim?s? rounded out his training in mathematics. He also studied medicine with al-Mirr?kh, but he did not delve deeply into the subject. The mystic al-Hazmir? was responsible for directing a great part of Ibn al-Bann??’s works to the study of the magic properties of numbers and letters.

He taught arithmetic, algebra, geometry, and astronomy in the madrasa al-?A???r?n in Fez. Among his disciples were Ab? Zayd ‘Abd al-Rahm?n... al-Laj??? (d.ca 771/1369) teacher of Ibn Qunfudh, who left us an excellent biographical sketch of Ibn al-Bannn??; mu?ammad ibn Ibr?h?m al-Ab?li (d 770/1368) Abu’l-Barak?t al-Bal?fiq? (d 771/1370), Who had ibn al-Kha??b and Ibn Khald?n as disciples; and Ibn al-Najj?r al-Tilims?n?.

H.P.J. Renaud lists eighty-two works by Ibn al-Bann??. The most important scientific ones are an introduction to Euclid; a treatise on areas; an algebra text dedicated to Ab? ?Al? al-?asan al-Mily?n? a book about acronical risings and settings (Kit?b al-anw??), which is not as good as his other works on astronomy, such as the Minh?j; and an almanac that is possibly the earliest known, in which the word man?kh appears for the first time in its Arabic form. The works of greatest merit, however, are the Talkh?s and the Minh?j.

The Talkh?? as its title indicates, is a summary of the lost works of the twelfth- or thirteenth-century mathematician al-?a???r. It was later summarized in verse by Ibn al-Q??i (d. 1025/1616) and was often commented on and glossed. Outstanding commentaries are the Raf?al-?ij?b by Ibn al-Bann?? himself, with notes by Ibn Hayd?r and that of al-Qala??d? 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-Qala??d?’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-Bann?? was responsible for introducing a system of mathematical notation.

The Kit?b minh?j al-??lib li ta?d?l al-kaw?kib is a very practical book for calculating astronomical ephemerals, thanks to the attached tables that are based upon those that Ibn Is??q al T?nis? calculated for the year 1222. The theoretical part does not contribute anything new and sometimes gives incorrect relationships between contradictory theories.

Ibn al-Bann?? is credited with a Ris?la (“epistle”) on the astrolabe called ?af??a shak?ziyya a variation of the ?af??a zarq?liyya or “al-Zarq?l?’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-Bann?? 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-Bann??,” 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 Talkh?? in Atti dell’ Accademia pantificia de Nuovi Linncei, 17 (5 July 1864); the commentary of al-Qala??d? was translated by M. F. Woepcke ibid12 (3 April 1859). The Minh?j has been edited, translated into Spanish, and Studied by J. Vernet (Tetuán, 1951). The Kit?b al-anw?? was edited, translated into French, and commented on by H.J.P. Renaud (Paris, 1948).

II. Secondary Literature. The Arabic sources for Ibn al-Bann??’s life are listed in al-Zirikl?, al-A?l?m, 2nd ed., I, 213–214; especially in H. P. J. Renaud, “Ibn al-Banna? de Marrakech ??f? et matheématicien,” in Hesperis25 (1938), 13–42 The muqaddima of Ibn khald?n 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-Bann??,” 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, tawq?m. 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