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This work is a versified treatise on arithmetic (*‘ilam al- ḥisāb*), and specifically the art of dividing inheritance (*farā’iḍ*), which has application in Islamic law. After a standard expression of praise for the Prophet, his companions, and later followers, the text introduces the system of place values and explains multiplication of multi-digit whole numbers and simple and compound fractions. The text presents multiple examples that are described in verbal terms. As noted at the end of the manuscript, which was completed on Monday, 20 Rabī‘ I of the year ...

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 treatise in this manuscript is a commentary on a mathematical treatise by Šihāb al-Dīn Aḥmad ibn Muḥammad Ibn al-Hā’im (circa 1355–1412). Ibn al-Hā’im taught mathematics and Islamic jurisprudence, subjects on which he wrote extensively. The erudite Badr al-Dīn Muhammad Sibt al-Māridīnī (circa 1423–1506), who was at the time working as *muwaqqit* (timekeeper) at the Al-Azhar mosque in Cairo, composed this short commentary less then 60 years after the death of Ibn al-Hā’im. Following widespread tradition in Islamic lands, Sibt al-Māridīnī included in the title ...

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 ...

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 ...

The system of *fara'i**ḍ *(shares) for inheritances is considered to be one of the most advanced innovations introduced by Muslim conquerors in Middle Eastern and North African societies. The exact calculation of shares of inheritance is a complex chapter in Islamic law, and it is not surprising that Muslim intellectuals and scientists developed a system of mathematical tools in order to master "the science of the shares" (*‘ilm al-fara'i**ḍ*). An important contribution to this field can be found in the work of Aḥmad ibn Muḥammad Ibn ...

This 18th-century manuscript offers a clear example of the continued use in the Islamic world of the scientific commentary well after the end of Middle Ages, the period most associated with Arabic scientific achievement and this literary form. In this case, the treatise commented upon is the *Nuzhat al-nuẓẓār fī ‘ilm al-ghubār *(The excursion of the observer in the science of numerals), which was itself an abridgment by Aḥmad ibn Muḥammad al-Farāḍī ibn al-Hā'im (around 1356-1412) of his own mathematical treatise entitled *Murshid al-ṭālib ilā asnā' al-maṭālib *(A student ...

The present manuscript preserves a copy of Aḥmad ibn Qāsim al-Shāfi‘ī al-Ġhazzī's *Kitāb sharḥ al-nuzha fī ‘ilm al-ḥisāb** *(The book of the explanation of the excursion in the science of calculus), a work that exemplifies the lively interest in the mathematical sciences that persisted in the Islamic world well after the end of the "classical" period that saw the flowering of Arabic sciences. *Kitāb sharḥ al-nuzha fī ‘ilm al-ḥisāb** *is technically a supercommentary. Al-Ġhazzī ’s work is an explanation of *Nuzhat al-nuẓẓār fī ‘ilm al-**ghubār *(The excursion ...

The Arabic mathematical tradition, which flourished during the Middle Ages, transmitted and enriched the knowledge derived from Greek and Indian sources. Arabic mathematicians further developed these studies, seeking to answer theoretical as well as practical problems. Medieval Arabic mathematical treatises were extensively copied, studied, and commented upon in subsequent centuries, as exemplified in this manuscript. This supercommentary (commentary on a commentary) by Aḥmad Muhammad al-Šāfiʻī al-Janājī al-Mālikī elucidates an earlier commentary by Zakarīyā ibn Muḥammad al-Anṣārī (circa 1420–1519) on a work by Aḥmad ibn Muḥammad al-Farāḍī ibn al-Hāʼim (circa ...

This manuscript is an 18th-century copy of *Nuzhat al-ḥisāb* (The excursion of calculus)* *by mathematician Aḥmad ibn Muḥammad al-Farāḍī ibn al-Hā'im (around 1356–1412). The copyist of this brief but densely written codex provided his name and the date of the completion of his work in the colophon: at the bottom of the last page of the manuscript is stated that Aḥmad ibn Qāsim ibn Aḥmad ibn Muḥammad al-Hanbalī finished this copy in the year 1185 AH (1772). The *Nuzhat al-ḥisāb** *is an abridgment by Ibn al-Hā'im of ...