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29 results
Unique Algebraic Remainders on the Sibṭ’s Commentary on the Yāsamīnīyya
This work is an elaboration of the commentary written by the Egyptian mathematician Sibṭ alMāridīnī—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 ‘AbdAllāh alIshbīlī alMarrakushī, also known as Ibn alYāsamīn, who died in 1204 (600 AH). AlYāsamīn summarized his mathematical knowledge in a versified treatise known as the Yāsamīnīyya (The treatise by alYāsamīn). Around the end of the 15th century, alYāsamīn’s verses were the object of a ...


The Recension of Euclid's "Elements"
This work is a printed edition of Kitāb taḥrīr uṣūl liUqlīdus (The recension of Euclid's Elements) by one of the intellectual luminaries of the Islamic world, the Persian polymath Naṣīr alDīn Muḥammad ibn Muḥammad alṬūsī (1201–74). After his death alṬūsī was referred to as almuʿallim althālith (the third teacher, with Aristotle and Fārābī referred to as the first and second teachers, respectively). An extraordinarily prolific author, alṬūsī made notable contributions to most of the intellectual fields of his era, writing on theology, mysticism, logic ...


A Friendly Gift on the Science of Arithmetic
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 ...


Commentary on the Gift of Arithmetic
This work is by AbdAllāh Ibn Bahā alDin Muhammad Ibn AbdAllāh alShanshāri alShāfīī, an expert in calculating alFardī (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 alahbāb fi alhisāb (The friendly gift of arithmetic) by the renowned Egyptian scholar Badr alDīn Muhammad Ibn Muhammad Ibn Ahmad (1423–1506), known as the Sibt (grandson of) alMardini, who taught arithmetic and astronomy in Alazhar for several years. The original work has an ...


Glosses of alHifnī on the Yāsamīnīyya
This work is an elaboration of the commentary written by the Egyptian mathematician Sibṭ alMāridīnī (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 ‘AbdAllāh alIshbīlī alMarrakushī, also known as Ibn alYāsamīn (died 1204 [600 AH]). Ibn alYāsamīn’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 ...


The Introductory Epistle on Sinusoidal Operations
This manuscript is a copy of alRisāla alFatḥīya fī ala‘māl aljaybīya (The introductory epistle on sinusoidal operations) by Muḥammad ibn Muḥammad ibn Aḥmad Abu ‘Abd Allāh, Badr alDīn (1423–1506), known as Sibṭ alMāridīnī or the grandson of alMāridīnī, 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 Lifting of the Veil in the Operations of Calculation
The establishment of the BerberMuslim 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 alBannā was born in the second half of the ...


The Desire of the Students for an Explanation of the Calculator's Craving
This manuscript offers a clear example of the liveliness of the North African mathematical tradition under the MuslimBerber dynasties that ruled over the Islamic West from the 12th century to the first half of the 17th century. They were the Almohads (12th–13th centuries), the Marinids (13th–15th centuries), the Wattasids (15th–16th centuries), and the Saadis (16th–17th centuries). While there was little scientific advance in other fields in this period, the mathematical sciences kept on developing, as reflected both in the composition of original works and in commentaries ...


Glosses of alHifnī on the Yāsamīnīyya
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 alYāsamīn summarized his mathematical knowledge in a versified treatise known as Yāsamīnīyya (The treatise ...


Facts on the Calculation of Degrees and Minutes
This manuscript by Badr alDīn Muhammad ibn Muhammad ibn Ahmad ibn Muhammad ibn alĠazal (1423–1506) contains a commentary on, and abridgement of, the astrological treatise on the calculation of the movement of stars and planets, Kašf alhaqā’iq fī hisāb aldaraj waaldaqā’iq (The uncovering of the facts regarding the calculation of degrees and minutes), by the Egyptian astronomer and mathematician Ahmad ibn Rağab ibn alMağdī (1366–1447). Ibn alMağdī was a disciple of the famous ‘Abdallāh alMāridīnī (or alMārdīnī), who was the grandfather of the author of this ...


Quintessence of Calculation
The author of this mathematical treatise, Bahā' alDīn Al‘Amilī (1547–1621), is considered one of the leading intellectuals of 17thcentury Safavid Persia (presentday Iran). He was born in Baalbek (presentday Lebanon) but moved to Persia in his youth where he devoted his entire life to study. He excelled in various fields, leaving a legacy of more than 80 books on a wide variety of subjects that included theology and mysticism, astronomy, mathematics, poetry, and architecture. He wrote in both Persian and Arabic. He was the teacher of Mulla Sadra ...


The Commentary on “The Little Sparkles on the Science of Calculation”
The treatise in this manuscript is a commentary on a mathematical treatise by Šihāb alDīn Aḥmad ibn Muḥammad Ibn alHā’im (circa 1355–1412). Ibn alHā’im taught mathematics and Islamic jurisprudence, subjects on which he wrote extensively. The erudite Badr alDīn Muhammad Sibt alMāridīnī (circa 1423–1506), who was at the time working as muwaqqit (timekeeper) at the AlAzhar mosque in Cairo, composed this short commentary less then 60 years after the death of Ibn alHā’im. Following widespread tradition in Islamic lands, Sibt alMāridīnī included in the title ...


The Abridged Commentary on "The Apple in the Science of Measurement"
This manuscript is a commentary on the treatise AlTuffāḥa fi ‘ilm alMisāḥa (The apple in the science of measurement), which was written at the beginning of the 12th century by the mathematician Aḥmad ibn Muḥammad alAšh‘ari. The study of measures and measurement techniques (‘ilm almisāha) was of great interest to Arabic mathematicians during the Middle Ages, both from theoretical and practical points of view. The ability to calculate the dimensions of landholdings was extremely important when it came to determining the correct amounts for inheritances and to calculating taxes ...


The Illumination of Inheritance Calculation
Islamic law goes into great detail on the subject of the division of inheritances (farā'id) among heirs. For this reason, inheritances have received extensive treatment in books of fiqh (Islamic law) and been a subject of study for mathematicians as well. Qabas alDaw' fī alHisāb (The illumination of inheritance calculation) was copied by its author, ‘Abd alRaḥman ibn Aḥmad ibn 'Ali alḤamidi, in this 1589 manuscript. The work, which he dedicated to the son of the Šāf‘ī jurist Šams alDīn Muhammad alBahwašī, is an example of a genre ...


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 Arabicspeaking countries that contain original treatises and commentaries. The work preserved in this manuscript, Nuzhat alHussāb alMuhtasara min alMuršida (The abridged amusement of the calculator from The guide), is a shorter version of Muršida fī Sina’at alGubar (The guide to the art of the numerals), an extensive treatise ...


The Little Sparkles on the Science of Calculation
The treatise preserved in this manuscript, AlLuma‘alyasīra fī ‘ilm alhisāb (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 Qur'an, verses 11–12, criticizes the traditional preIslamic system of agnatic succession, under which only men could inherit property, and provides for a proportional division among all the heirs, women included ...


The Shimmer of AlMāridinī in the Explanation of the Treatise by alYāsamīn
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 alDīn Muḥammad ibn Muḥammad ibn alĠazal, best known as Sibṭ alMāridīnī ("the son of alMāridīnī’s daughter") from the name of his famous maternal ancestor, who was also a mathematician. The Lum‘a alMāridīnīyya is an extensive prose commentary on a famous poem on algebra composed by the Maghrebi mathematician alYāsamīn around the last ...


The Shimmer of AlMāridinī in the Explanation of the Treatise by alYāsamīn
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 alDīn Muḥammad ibn Muḥammad ibn alĠazal, best known as Sibṭ alMāridīnī ("the son of alMāridīnī’s daughter") from the name of his famous maternal grandfather, who was himself a mathematician. Sibṭ alMāridīnī's mathematical ...


The Shimmer of AlMāridinī in the Explanation of the Treatise by alYāsamīn
The 12thcentury mathematical poem known as alYāsamīnīyya fī ‘ilm alJabr (The poem by alYāsamīn on calculus) from the name of its author, alYāsamīn, 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 20thcentury copy of the 15thcentury commentary on the Yāsamīnīyya written by Badr alDīn Muḥammad ibn Muḥammad ibn alĠazal, best known as Sibṭ alMāridīnī ("the son ...


Commentary on "The Little Sparkles on the Science of Calculation"
The system of fara'iḍ (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 alfara'iḍ). An important contribution to this field can be found in the work of Aḥmad ibn Muḥammad Ibn ...


The Explanation of the Abridgment on Calculus
The present manuscript preserves an extensive commentary on the 17thcentury mathematical treatise AlḪulāṣa fī alḤisāb (The abridgment on calculus), which was composed by Bahā' alDīn Al‘Amilī (1547–1621), one of the leading intellectuals of 17th century Safavid Persia (presentday Iran). Born in the city of Baalbek (presentday Lebanon), Al‘Amilī was an important figure in many different fields of knowledge, including theology, mysticism, poetry, astronomy, mathematics, and architecture. His main contribution to mathematics, the AlḪulāṣa fī alḤisāb, was well known and is the subject of the commentary by ...
