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30 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 Threefold Lily of Practical Arithmetic
Johannes Huswirth (Sanensis) was a German arithmetician who flourished around 1500. Nothing is known of his life. That he is sometimes referred to as Sanensis suggests that he may have come from Sayn, Germany. Arithmetice Lilium Triplicis Practice (The threefold lily of practical arithmetic) presents basic arithmetic operations such as addition and multiplication for whole numbers and fractions. It treats much of the same material that Huswirth had covered in an earlier work, Enchirdion Algorismi (Handbook of algorithms). The work includes two woodcut illustrations; one of God the Father and ...


Sakhāqī’s Book [of Arithmetic]
This work is a tutorial text on elementary arithmetic, in 20 folios. It is divided into an introduction, 11 chapters, and a conclusion. In the beginning, the sign for zero is introduced, along with the nine Indian numerals, written in two alternative forms. This is followed by a presentation of the place system. The first four chapters cover, respectively, addition, subtraction, multiplication, and division. Chapter five introduces operations on nonwhole numbers. The remaining six chapters discuss fractions and operations on them.


Easing the Difficulty of Arithmetic and Planar Geometry
This work is a comprehensive tutorial guide on arithmetic and plane geometry, in 197 folio pages. It also discusses monetary conversion. The work is composed in verse form, and is meant as a commentary on existing textbooks. The author gives the following personal account of the writing of this guide: In Rajab 827 A.H. (May 1424) he traveled from Damascus to Quds alSharīf (in Palestine), where he met two scholars named Ismā‘īl ibn Sharaf and Zayn alDīn Māhir. There he took lessons on arithmetic, using an introductory book ...


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 ...


The Light of the Glitter in Mathematics
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 multidigit 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 ...


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 Best of Arithmetic
This treatise on the art of arithmetic, completed in the late 1880s, opens a window into the early interaction between traditional and modern mathematical pedagogy in Egypt. The use of French loan words, such as million, along with some modern notation, indicates the author’s familiarity with developments in the teaching of arithmetic at the time. The work has an introduction followed by ten chapters and a conclusion. Following traditional praise for God, the Prophet Muhammad, and virtuous vanguards of learning, the treatise opens by introducing arithmetic as a useful ...


Guidebook for Students on the Use of Arithmetic
This guidebook is a short commentary on a work on arithmetic entitled alWasīla (The tool) completed in the 14th century by Shihāb alDīn Ahmad ibn Alī ibn Imād. The commentary is by the renowned Egyptian scholar known as Sibt (grandson of) alMāridīnī (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 alChalabī alHanafī in 1496 (AH 903) at the ...


Bulgarian Arithmetic
Arithmetics were a popular genre of textbooks during the era of the Bulgarian National Revival in the 19th century, when it was widely believed that everyone, especially future businessmen, needed to know basic mathematics. Bulgarian Arithmetic was the fourth such text published in this era, in 1845. The author, Khristodul Kostovich SichanNikolov (1808–89), was a monk, teacher, writer, and publicist, often assisted in his scholarly pursuits by the writer, educator, and priest Neofit Rilski. Before writing his own text, SichanNikolov had been involved as the editor of the first ...


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 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 ...
