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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 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 ...
On the Sphere and the Cylinder; On the Measurement of the Circle; On Conoids and Spheroids; On Spirals; On the Equilibrium of Planes; On the Quadrature of the Parabola; The Sand Reckoner
In the middle of the 15th century, a number of manuscripts by the third-century BC Greek mathematician Archimedes began to circulate in the humanistic centers in the courts of Italy. Piero della Francesca (circa 1416–92), the Renaissance artist best known for the frescos he painted for the Vatican and for the chapels in Arezzo, transcribed a copy of a Latin translation of Archimedes’s geometry (a compilation of seven surviving treatises) and illustrated it with more than 200 drawings representing the mathematical theorems in the texts. This manuscript, long ...
The Recension of Euclid's "Elements"
This work is a printed edition of Kitāb taḥrīr uṣūl li-Uqlīdus (The recension of Euclid's Elements) by one of the intellectual luminaries of the Islamic world, the Persian polymath Naṣīr al-Dīn Muḥammad ibn Muḥammad al-Ṭūsī (1201–74). After his death al-Ṭūsī was referred to as al-muʿallim al-thālith (the third teacher, with Aristotle and Fārābī referred to as the first and second teachers, respectively). An extraordinarily prolific author, al-Ṭūsī made notable contributions to most of the intellectual fields of his era, writing on theology, mysticism, logic ...
Treatise on the Craft of Weight Measurement
This work is a treatise on the construction and use of the weighing balance (qabān, also qapān). It brings together geometric, mechanical, and arithmetic knowledge needed to construct and utilize measuring devices for weighing heavy and irregularly-shaped objects. The author’s name is unknown, but excerpts from another work by an already-deceased Shaykh ‘Abd al-Majīd al-Shāmulī al-Maḥallī are quoted in the treatise. The last page of the manuscript contains a sheet of verses that describe the basics of using a weighing balance, in a form that is easy to remember ...
Guide to Operations on Irrational Radicals for Neophytes
This mathematical treatise by Muḥammad b. Abi al-Fatḥ Muḥammad b. al-Sharafī Abi al-Rūḥ ‘Īsā b. Aḥmad al-Ṣūfī al-Shāfi‘ī al-Muqrī, was written in 1491-92 (897 AH). It begins with a "General Introduction," followed by two main parts, with a concluding section on the study of cubes and cube roots. Part I, "Operations on Simple Irrational Radicals," is divided into four chapters. Chapter 1 covers simplification of radicals. Chapters 2, 3, and 4 deal respectively with the multiplication, addition and subtraction, and division of radicals. Part II, on "Operations with Compound ...
Comprehensive Reference on Algebra and Equations
This manuscript is a didactic work on arithmetic and algebra, composed in versified form, as a qasīda of 59 verses. It was composed by Ibn al-Hā’im al-Fardī in 1402 (804 A.H.). The beginning of the work also names ‛Alī b. ‛Abd al-Samad al-Muqrī al-Mālikī (died Dhu al-Ḥijja 1381 [782 A.H.]), a scholar and teacher who had come to Egypt and taught at the ‛Amr b. ‛As madrasa for several years. The main part of the qasīda begins by introducing and defining key terms in arithmetic and algebra ...
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 non-whole 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 al-Sharīf (in Palestine), where he met two scholars named Ismā‘īl ibn Sharaf and Zayn al-Dīn Māhir. There he took lessons on arithmetic, using an introductory book ...
The Book of Instruction on Deviant Planes and Simple Planes
This manuscript is a work on practical astronomy and the drawing of the circle of projection and related concepts from spherical trigonometry. It is rich with geometric diagrams, tables of empirical observations, and computations based upon these observations. An interesting feature of the manuscript is the appearance on the margins of the cover, and on several pages in the manuscript, of edifying verses, proverbs, and witty remarks. One reads, for example, “It is strange to find in the world a jaundiced physician, a dim-eyed ophthalmologist, and a blind astronomer.” Most ...
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 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 ...
The Fathiyya Essay on Using the Mughayyab Quadrant
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 ...
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 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 ...
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.
Glosses of al-Hifnī on the Yāsamīnīyya
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 ...
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 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 ...
The Introductory Epistle on Sinusoidal Operations
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 ...
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 Sichan-Nikolov (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, Sichan-Nikolov had been involved as the editor of the first ...
The Lifting of the Veil in the Operations of Calculation
The establishment of the Berber-Muslim 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 al-Bannā 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 Muslim-Berber 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 ...