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This work is an elaboration of the commentary written by the Egyptian mathematician Sibṭ al-Māridīnī—i.e., a commentary on another commentary—on the *urjūzah* (versified introduction) to the science of algebra, originally composed by the Berber mathematician and man of letters Abū Muḥammad ‘Abd-Allāh al-Ishbīlī al-Marrakushī, also known as Ibn al-Yāsamīn, who died in 1204 (600 AH). Al-Yāsamīn summarized his mathematical knowledge in a versified treatise known as the Yāsamīnīyya (The treatise by al-Yāsamīn). Around the end of the 15th century, al-Yāsamīn’s verses were the object of a ...

This work, by a timekeeper at the Al-Azhar Mosque in Cairo, is an important and comprehensive textbook on timekeeping. It introduces the useful device of dividing a quarter of a circle of projection into sections known as *almucantars* (*muqanṭarāt*). The work, comprising 100 folio pages, contains 30 chapters and a conclusion. The work was composed in 1440-1 (844 A.H.) and was copied in 1757 (1170 A.H.).

This treatise deals specifically with basic arithmetic, as needed for computing the division of inheritance according to Islamic law. It contains 48 folios and is divided into an introduction, three chapters, and a conclusion. The introduction discusses the idea of numbers as an introduction to the science of arithmetic. Chapter I discusses the multiplication of integers. Chapter II is on the division of integers and the computation of common factors. Chapter III deals extensively with fractions and arithmetic operations on them. The author, an Egyptian jurist and mathematician, was the ...

This work is by Abd-Allāh Ibn Bahā al-Din Muhammad Ibn Abd-Allāh al-Shanshāri al-Shāfīī, an expert in calculating al-Fardī (inheritance portions). The cover page of the manuscript bears a magical form or talisman for finding a lost object. The main text is a detailed commentary on *Tuhfat al-ahbāb fi al-hisāb* (The friendly gift of arithmetic) by the renowned Egyptian scholar Badr al-Dīn Muhammad Ibn Muhammad Ibn Ahmad (1423–1506), known as the Sibt (grandson of) al-Mardini, who taught arithmetic and astronomy in Alazhar for several years. The original work has an ...

This treatise by Badruddin al-Maridini (died 1506 [912 AH]), better known as Sibt al-Maridini, includes an introduction, 20 sections, and a conclusion. The treatise discusses a range of issues in astronomy, surveying, and mathematics. It describes the sine quadrant and parallel circles, and explains how to measure the width of a river, the angle of a star, the depth of a well, or the height of a mountain. Al-Maridini, whose parents were from Damascus, was born, raised, and educated in Cairo late in the Mamluk Dynasty (1250–1517). The manuscript ...

This work is an elaboration of the commentary written by the Egyptian mathematician Sibṭ al-Māridīnī (i.e., a commentary on another commentary), on the versified introduction, or *urjūzah*, to the science of algebra, originally composed by the Berber mathematician and man of letters Abū Muḥammad ‘Abd-Allāh al-Ishbīlī al-Marrakushī, also known as Ibn al-Yāsamīn (died 1204 [600 AH]). Ibn al-Yāsamīn’s work has not been examined in detail by scholars, so the apparent inclusion in this treatise of original lines by Ibn Yasamīn is of great importance in studying his contribution ...

This guidebook is a short commentary on a work on arithmetic entitled *al-Wasīla *(The tool) completed in the 14th century by Shihāb al-Dīn Ahmad ibn Alī ibn Imād. The commentary is by the renowned Egyptian scholar known as Sibt (grandson of) al-Māridīnī (1423–1506), who taught mathematical sciences at Alazhar for a long time. The body of the work begins with a general discussion on numbers, and forms a standard introduction to arithmetic. The manuscript, which was completed by Ahmad ibn Yūnus al-Chalabī al-Hanafī in 1496 (AH 903) at the ...

This manuscript is a copy of *al-Risāla al-Fatḥīya fī al-a‘māl al-jaybīya* (The introductory epistle on sinusoidal operations) by Muḥammad ibn Muḥammad ibn Aḥmad Abu ‘Abd Allāh, Badr al-Dīn (1423–1506), known as Sibṭ al-Māridīnī or the grandson of al-Māridīnī, in honor of his mother’s father, a famous astronomer. The manuscript consists of 16 pages of 14 lines each, and includes an introduction and 20 *bābs* (chapters or articles). They range in length from a few lines to a page, and cover such topics as determination of the cardinal ...

The mathematical tradition that developed in North Africa during the Middle Ages continued to attract the interest of scholars in subsequent centuries. Medieval treatises were extensively read and made the subject of commentaries. In many cases, these commentaries became the object of other works—or supercommentaries—aimed at further clarifying the subject of the original treatises. This manuscript is an example of this phenomenon. In the 12th century, the North African mathematician ‘Abdallāh ibn Hajjāj ibn al-Yāsamīn summarized his mathematical knowledge in a versified treatise known as Yāsamīnīyya (The treatise ...

This manuscript by Badr al-Dīn Muhammad ibn Muhammad ibn Ahmad ibn Muhammad ibn al-Ġazal (1423–1506) contains a commentary on, and abridgement of, the astrological treatise on the calculation of the movement of stars and planets, *Kašf al-haqā’iq fī hisāb al-daraj wa-al-daqā’iq* (The uncovering of the facts regarding the calculation of degrees and minutes), by the Egyptian astronomer and mathematician Ahmad ibn Rağab ibn al-Mağdī (1366–1447). Ibn al-Mağdī was a disciple of the famous ‘Abdallāh al-Māridīnī (or al-Mārdīnī), who was the grandfather of the author of this ...

The challenge of calculating the positions and movements of celestial bodies for the purpose of preparing astronomical tables helped to stimulate the development of very sophisticated mathematical tools at least as far back as the Middle Ages. The link between mathematics and astronomy was so strong that important authors in the field of astronomy were often distinguished mathematicians and vice versa. This was the case with Badr al-Dīn Muhammad ibn Muhammad ibn Ahmad ibn Muhammad ibn al-Ġazal (1423–1506), also known as Sibt al-Māridīnī, who, according to contemporary sources, produced ...

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 ...

The present manuscript preserves a very elegant copy of a work by one of the most prolific authors of the second half of the 15th century in the field of mathematics and related subjects: Badr al-Dīn Muḥammad ibn Muḥammad ibn al-Ġazal, best known as Sibṭ al-Māridīnī ("the son of al-Māridīnī’s daughter") from the name of his famous maternal ancestor, who was also a mathematician. The *Lum‘a al-Māridīnīyya *is an extensive prose commentary on a famous poem on algebra composed by the Maghrebi mathematician al-Yāsamīn around the last ...

The mathematical tradition that flourished in North Africa and Andalusia during the Middle Ages did not undergo the same decline that many scholars claim occurred in the sciences after the first half of the 13th century. The present work supports this point. The manuscript is a very elegant copy of a mathematical text by Badr al-Dīn Muḥammad ibn Muḥammad ibn al-Ġazal, best known as Sibṭ al-Māridīnī ("the son of al-Māridīnī’s daughter") from the name of his famous maternal grandfather, who was himself a mathematician. Sibṭ al-Māridīnī's mathematical ...

The 12th-century mathematical poem known as *al-Yāsamīnīyya fī ‘ilm al-Jabr *(The poem by al-Yāsamīn on calculus) from the name of its author, al-Yāsamīn, is one of the most read and commented upon mathematical texts of its time. Its verses have been extensively copied, both in autonomous form and by incorporation into larger commentaries up to the 20th century. The present manuscript preserves an early 20th-century copy of the 15th-century commentary on the *Yāsamīnīyya* written by Badr al-Dīn Muḥammad ibn Muḥammad ibn al-Ġazal, best known as Sibṭ al-Māridīnī ("the son ...

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 supercommentary (commentary on a commentary) by Aḥmad Muhammad al-Šāfiʻī al-Janājī al-Mālikī testifies to the liveliness and endurance of the Arabic mathematical tradition and demonstrates the continuous exegetical effort in which Arabic scientists commented upon previous works with the aim of expanding and clarifying their contents. The North African mathematician ‘Abd Allāh ibn Ḥajjāj ibn al-Yāsamīn (died 1204) conveyed his mathematical knowledge in a poem known as *Yāsamīnīyya* (The treatise by al-Yāsamīn). Al-Yāsamīn’s verses became the subject of a prose commentary, the *Lum‘a al-Maridinīyya fī** Šarḥ al-Yāsamīnīyya *(The ...