Commentary by Islam's Sheikh Zakariyya al-Ansari on Ibn al-Hā’im's Poem on the Science of Algebra and Balancing Called the Creator's Epiphany in Explaining the Cogent

This work is a commentary on a versified, 59-line introduction to algebra, entitled Al-Muqni‘ fī al-jabr wa al-muqābila, by the prolific and influential mathematician, jurist, and man of letters Abū al-‘Abbās Shihāb al-Dīn Aḥmad ibn Muḥammad ibn ‘Alī al-Maqdisī al-Shāfi‘ī, known as Ibn al-Hā’im (circa 1356-1412 [circa 753-815 AH]). It clarifies the nomenclature and explains the basic concepts of algebra, and provides succinct examples. The manuscript, completed on Thursday night, 8 Sha‘bān 1305 AH (March 21, 1888), is in the hand of Tāhā ibn Yūsuf.

The Little Sparkles on the Science of Calculation

The treatise preserved in this manuscript, Al-Luma‘al-yasīra fī ‘ilm al-hisāb (The little sparkles on the science of calculation), deals with Muslim inheritance. Of the social innovations that came with the Islamic conquest, the introduction of the system of fara'id (shares) for inheritances was one of the most radical and socially advanced. The fourth surah of the Qurʼan, verses 11–12, criticizes the traditional pre-Islamic system of agnatic succession, under which only men could inherit property, and provides for a proportional division among all the heirs, women included. The exact reckoning of the shares of inheritance became a delicate and complex subject within Islamic law, and Muslim intellectuals devised mathematical tools to simplify the calculations implied in the ‘ilm al-fara'id (the science of the shares). This work, written in the last years of the 14th century, is a contribution on this subject by Aḥmad ibn Muḥammad ibn al-Ha’im (1356–1412). The treatise is not confined to problems of inheritance: Ibn al-Ha’im introduces his arguments with extensive passages on numbers, their types and different features, and devotes most of the work to discussing multiplication (darb) and division (qisma).

The Abridged Amusement of the Calculator from "The Guide"

Much traditional scholarship holds that the period after about 1250 saw a decline in the production of scientific and philosophical works in the Arab world. This view is challenged by the impressive number of manuscripts written after that date in different Arabic-speaking countries that contain original treatises and commentaries. The work preserved in this manuscript, Nuzhat al-Hussāb al-Muhtasara min al-Muršida (The abridged amusement of the calculator from The guide), is a shorter version of Muršida fī Sina’at al-Gubar (The guide to the art of the numerals), an extensive treatise on arithmetical operations written by Aḥmad ibn Muḥammad ibn al-Ha’im (1356–1412) around the end of the 14th century. After completing his studies in Cairo, Ibn al-Hāʼim left for Jerusalem, where he worked as a teacher of mathematics until his death. Several of his works, and especially the Nuzhat al-Hussāb, have a clear educational aim. The introductory section, in which the author describes the Hindi numerals and their correspondences with the traditional Arabic alphabetical numeration (abjad), is followed by a lengthy exposition on the four arithmetical operations: addition (jam‘), subtraction (tarh), multiplication (darb), and division (qisma). Ibn al-Ha’im's activity as a professor did not prevent him from devising particularly witty solutions for mathematical problems: he is credited with the discovery of a method for solving general second-degree equations without using divisions of fractions.