The Lifting of the Veil in the Operations of Calculation


The establishment of the Berber-Muslim dynasty of the Almohads in North Africa and Andalusia in the 12th century coincided with the decline in scientific advances in many fields of knowledge, including medicine. This was not the case with mathematics, and the treatise preserved in this manuscript together with other works by the same author stand as clear proof of the liveliness of this field under the rule of the Almohads and of the Marinid dynasty that followed. Abū ‛Abbās Ahmad Ibn al-Bannā was born in the second half of the 13th century in Marrakesh and spent most of his life working as a teacher in the city of Fez. His interests were not limited to mathematics: he produced an introduction to Euclidean geometry and compiled astronomical tables for the calculation of planetary longitudes, together with treatises on logic, linguistics, and rhetoric. Moreover, he was an active member of the Sufi confraternity of the Hazmīrīya. The biographer Ahmād ibn Šātir (died, 1375) went so far as to attribute to al-Bannā the performance of miracles. The present work is an extensive commentary in two parts on another treatise by al-Bannā, the Talhīs ‘amal al-hisāb (The abridgement of the operations of calculation). The complexity of that work was recognized by the famous 14th-century historiographer Ibn Haldūn, who described the treatise in his Muqaddima (Introduction) as “very difficult for beginners, because of its rigor and the strict sequence of the demonstrations.” In the present commentary, Ibn al-Bannā explains in detail complex mathematical operations, including combinational computation, extended fractions, arithmetic series, and binomial coefficients and provides a philosophical and theological framework for his mathematical discourse.

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Title in Original Language

كتاب رفع الحجاب عن وجوه اعمال الحساب

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Physical Description

54 leaves (25 lines), bound : paper ; 21 x 14 centimeters


  • Paper: yellowed cream, with watermarks, in good condition; loose from spine. Red and black ink on title page, text is principally black, with some words in red. Occasional diacritical marks, some marginal notes, catchwords on rectos. Binding: modern cardboard covered with cloth; leather spine. Naskhī script with titles of chapters in Thuluth.


Last updated: September 18, 2015