The volume D'al-Khwārizmī à Descartes is a monumental contribution to the world history of mathematical sciences, showing clearly that Arabic mathematics was an indispensable predecessor of early modern European mathematics. Roshdi Rashed is known, first of all, as an editor of classical mathematical writings in Arabic by such authors as al-Khwārizmī, Thābit ibn Qurra, Ibrāhīm ibn Sinān, Ibn al-Haytham, al-Khayyām, Sharaf al-Dīn al-Ṭūsī, as well as of the Arabic versions of Apollonius' Conics , Diophantus' Arithmetica , and Diocles' (...) Burning Mirrors . As the volume under review shows, he is also a historian of mathematics of the first class who has transformed historiography. This book is, in a sense, a manifesto of Prof. Rashed's entire œuvre. (shrink)

In this paper, we analyze the astronomical tables in al-Zīj al-Muqtabis by Ibn al-Kammād (early twelfth century, Córdoba), based on the Latin and Hebrew versions of the lost Arabic original, each of which is extant in a unique manuscript. We present excerpts of many tables and pay careful attention to their structure and underlying parameters. The main focus, however, is on the impact al-Muqtabis had on the astronomy that developed in the Iberian Peninsula and the Maghrib and, more generally, on (...) the transmission and diffusion of Indian astronomy in the West after the arrival of al-Khwārizmī’s astronomical tables in al-Andalus (Muslim Spain) in the tenth century. This tradition of Indian origin competed with the Greek tradition represented by al-Battānī’s astronomical tables and was much more alive in the Iberian Peninsula and the Maghrib than previously thought. From Spain, the Indian tradition entered mainstream European astronomy, where we find echoes of it in all versions of the Alfonsine Tables, both in manuscript and in the printed editions (beginning in 1483), as well as in Copernicus’s De Revolutionibus, published in 1543. (shrink)

Extensive scientific, philosophical and artistic activities were carried out in the Islamic World’s various science and civilization centers during the early Middle Ages. In these centers, noteworthy works of mathematics, astronomy, geography, medicine, pharmacology, optics, botany, chemistry and other fields of science, which would later determine improvement paths for these fields, were created. Abu al-Izz Ismail ibn al-Razzaz al-Jazari (12th-13th centuries), was a magnificent Muslim scientist known for his work named The Book of Knowledge of Ingenious Mechanical Devices (Kitab fi (...) ma‘rifati’l-hiyal al-handasiyya) and he was born in geography where many scientists were trained. He contributed to the development of science and civilization, the joint legacy of humanity and demonstrated his true capability and success in the field of ilm al-hiyal (the scientific field which addresses the information and practices regarding mechanical technology and engineering in Islamic science history). From this perspective, it is evident that al-Jazari had a wide field of interest, made his mark in the age he lived in with his brave and innovative ideas, and was a wise engineer. al-Jazari’s detailed descriptions and explanations of water clocks, oil lamp clocks and water pumping machines, as well as their construction, were astounding. In addition, al-Jazari’s studies on metal casting techniques, cone valves, wheel balance and the real-world use of aspiration tubes are important in contemporary engineering studies. When all these are considered, it becomes clear that his designation as the “Leonardo da Vinci of the Islamic World” is not a coincidence. Many studies on al-Jazari’s scientific legacy have been conducted in various parts of the world. There are various manuscripts of his aforementioned book. Based on these manuscripts, the work has been -fully or partially- translated into many languages, including Turkish. The German and English translations served as a basis for studies on al-Jazari in other languages. In recent years, studies conducted on al-Jazari in Türkiye (books, articles, domestic and international symposiums, congresses etc.) have demonstrated his brilliance and competence as a scientist. Furthermore, studies on al-Jazari are still ongoing in Türkiye. As for Russia, the scientific legacy of the scientists raised in the Islamic World such as Avicenna, al-Farabi, Abu Bakr al-Razi, Abu Rayhan al-Biruni, Abu al-Qasim al-Zahrawi, Muhammad ibn Musa al-Khwarizmi, al-Battani, al-Kashi, Abd al-Rahman al-Khazini, Nasir al-Din al-Tusi was researched within the scope of a special plan and program. Depending on the relevant studies, al-Jazari and his work drew attention as well. A small portion of the aforementioned Russian studies is known in Türkiye. It is safe to assume that al-Jazari studies in Russia are virtually unknown in Türkiye. The present study primarily aims to contribute to the literature on the scientific legacy of al-Jazari, a Middle Age Islamic scientist best known for his famous work in the mechanical field. More specifically, the present study aims to: 1) to identify the studies on al-Jazari in Russia, and in the former USSR countries, where academic studies are still in Russian after the Soviet Union period, to create a chronological biography and to set forth their compilation; in other words, to create a bibliography which includes Russian studies on al-Jazari; 2) to provide information on the structure and content of the studies in question, to detect the methodological issues encountered in these works, and make solution recommendations to solve these issues; 3) to contribute to continuing and future studies in Türkiye on al-Jazari in terms of source and material index. In conclusion, it should be stated that comparative reading was conducted centered on The Book of Knowledge of Ingenious Mechanical Devices (Kitab fi ma‘rifati’l-hiyal al-handasiyya). It should also be noted that Russian popular internet publications (which are not based on academic research and are created/reproduced for commercial and personal purposes) were excluded from the assessment. (shrink)

Es común escuchar que el mundo Occidental debe a los árabes el descubrimiento del álgebra. No obstante, el desarrollo de esta disciplina puede interpretarse como un crisol de distintas tradiciones científicas que fue posible gracias a la clasificación, traducción y crítica tanto de los clásicos como de las obras que los árabes obtuvieron de los pueblos que conquistaron. Entre estos trabajos se encontraba Los Elementos de Euclides. Los Elementos fueron cuidadosamente traducidos durante el califato de Al-Ma’mūn por el matemático Mohammed (...) ibn-Musa Al-Khwārizmī, autor de Al-jabr wa’l muqābalah, quien sentó los fundamentos de la disciplina que más tarde sería conocida como álgebra y quien, en la primera parte de su obra, nos proporciona tres métodos para resolver tres tipos de ecuaciones que llama “ecuaciones combinadas”. A lo largo de este artículo se ofrecen argumentos para sostener que los métodos para resolver estas ecuaciones constituyen una reinterpretación, en el terreno algebraico, de los teoremas 6, 7 y 8 del segundo libro de Los Elementos de Euclides. Mi objetivo es dar respuesta a la siguiente pregunta: ¿Qué lectura de Los elementos Euclides posibilitó la emergencia del álgebra en el mundo árabe? Para responderla necesario explorar el acercamiento que los árabes tuvieron con el Libro II de Los Elementos, con el fin de proponer una interpretación de los posibles factores que los llevaron a formular el álgebra. Esto último, en particular, se encuentra en la primera parte de la obra de Al-Khwārizmī. Palabras clave: Álgebra, Al-Khwārizmī, Euclides, Ecuación, Teorema. (shrink)

The Prophet, whom Allah sent the whole universe and humanity as mercy, produced not only many judicial rules and practices regarding the relations of a person with Allah and other people in Islam but also uttered sentences about the explanation of holy book, Qur’an, and about how this book can be put into practice. The issue whether and how much these sentences of the prophet (hadith) and acts of the prophet (Sunnah) are binding have been discussed by both hadith methodologists (...) and fiqh methodologists; accordingly, a great many studies were produced. In hadith methodology, the discussions about Sunnah of the Prophet had their reflections in the studies of fiqh methodology; and especially Hanafi jurists propounded considerations about this issue. Hussein b. Ali al-Saymerî (d. 436/1045) one of these jurists, is the student of Muhammad b. Mûsa al-Khwârizmî (d. 403/1012), who is the student of Abû Bakr al-Jassâs (d. 370/980), who is an authority in Hanafi methodology. al-Saymerî, who adopted the method of al-Jassâs in fiqh methodology, systematically categorized several fundamental issues which were discussed and were related to fiqh methodology during his time; and he defended the views of Hanafi scholars about these issues primarily against Shâfiʿîs and several fiqh and kalam schools. While presenting the views and evidences of Hanafis, al-Saymerî initially applied for the views of founder imams of Hanafi sect such as Abû Hanîfa, Abû Yusuf and Muhammad al-Shaybânî; following these scholars, he greatly benefited from Hanafi scholars from Iraq region, such as Abu’l-Hasan al-Karkhî (d. 340/952) and his student, Abu Bakr al-Râzî al-Jassâs. When the relevant parts of his study is analysed, it is seen that the effect of al-Jassâs is especially noticeable. In this article, we will study the binding issue of the Sunnah of the Prophet within the context of al-Saymerî’s study, which has extant and is called Mesâilu’l-hilâf fi usûli’l-fiqh. We consider that the different attitude of al-Saymerî about the Sunnah of the Prophet from the other methodologists and hadith scholars and the underlying reasons of these differences are worth to be investigated and emphasized. (shrink)

ArgumentFrom the time of al-Khwārizmī in the ninth century to the beginning of the sixteenth century algebraists did not allow irrational numbers to serve as coefficients. To multiply$\sqrt {18} $byx, for instance, the result was expressed as the rhetorical equivalent of$\sqrt {18{x^2}} $. The reason for this practice has to do with the premodern concept of a monomial. The coefficient, or “number,” of a term was thought of as how many of that term are present, and not as the (...) scalar multiple that we work with today. Then, in sixteenth-century Europe, a few algebraists began to allow for irrational coefficients in their notation. Christoff Rudolff was the first to admit them in special cases, and subsequently they appear more liberally in Cardano, Scheubel, Bombelli, and others, though most algebraists continued to ban them. We survey this development by examining the texts that show irrational coefficients and those that argue against them. We show that the debate took place entirely in the conceptual context of premodern, “cossic” algebra, and persisted in the sixteenth century independent of the development of the new algebra of Viète, Decartes, and Fermat. This was a formal innovation violating prevailing concepts that we propose could only be introduced because of the growing autonomy of notation from rhetorical text. (shrink)

This article describes how the decimal place value system was transmitted from India via the Arabs to the West up to the end of the fifteenth century. The arithmetical work of al-Khwārizmī's, ca. 825, is the oldest Arabic work on Indian arithmetic of which we have detailed knowledge. There is no known Arabic manuscript of this work; our knowledge of it is based on an early reworking of a Latin translation. Until some years ago, only one fragmentary manuscript of (...) this twelfth-century reworking was known. Another manuscript that transmits the complete text has made possible a more exact study of al-Khwārizmī's work. This article gives an outline of this manuscript's contents and discusses some characteristics of its presentation. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:A Humanist History of Mathematics?Regiomontanus's Padua Oration in ContextJames Steven ByrneIn the spring of 1464, the German astronomer, astrologer, and mathematician Johannes Müller (1436–76), known as Regiomontanus (a Latinization of the name of his hometown, Königsberg in Franconia), offered a course of lectures on the Arabic astronomer al-Farghani at the University of Padua. The only one of these to survive is his inaugural oration on the history and utility (...) of the mathematical arts.1 Regiomontanus tells his audience that the purpose of the oration is torelate first the origin of our arts, and among which nations they first began to be cultivated, in what way they were at last translated from various foreign tongues into Latin, which of our ancestors were famed in these disciplines, and to whom in our lifetimes recognition should be granted.2To this end, he offers a history of the quadrivial arts (arithmetic, geometry, music, and astronomy) and other important mathematical disciplines from [End Page 41] antiquity to his own time, praises their utility, and exhorts his audience to revive the languishing study of mathematics at Padua. Astrology, a discipline with which Regiomontanus himself was closely associated, is singled out for particular praise.Traditionally, Regiomontanus's Padua oration has been seen through the lens of its rather obvious humanism. In particular, the Padua oration has come to be understood as the rhetorical embodiment of the fifteenth-and-sixteenth-century revival of ancient (Greek) mathematics. Just as this revival is inextricable from the rise of humanism, so Regiomontanus has come to be seen as an exemplar of humanist mathematics.3 It is the aim of this paper to examine the Padua oration in the context both of contemporary humanist rhetoric and of Regiomontanus's own intellectual background in order to argue that, while the oration is stylistically consistent with humanist norms, the vision of mathematics presented in it is also deeply grounded in the university mathematical curriculum and in Regiomontanus's own reading of mathematical texts.Regiomontanus was educated primarily at the University of Vienna (he was also briefly at the University of Leipzig), where he enrolled in 1450, completed his baccalaureate in 1452 and became a master in 1457.4 He remained at Vienna until 1461, when the death of his friend and teacher Georg Peurbach prompted him to travel to Italy with his patron, Cardinal Bessarion.5 In Regiomontanus's day Vienna was probably the most important of the German universities, rivaled only by Prague, whose prestige had declined after it was stripped of its theology faculty in the aftermath of the Hussite Wars.6 The curriculum at the University of Vienna was modeled [End Page 42] after that of Paris, and Parisian scholars played a major role both in its founding in 1365 and in its re-establishment (this time with a theology faculty) in 1384.7Most importantly for the purposes of this paper, the Viennese mathematical curriculum of Regiomontanus's day included all of the traditional authorities taught at Paris in the fourteenth century. For arithmetic and algebra, various "algorisms" (prose or poetry instructions for carrying out arithmetical operations that often also included a small amount of number theory) were the basic texts, supplemented in the fourteenth century by the Quadripartitum numerorum of Jean de Murs. Jordanus de Nemorare's De numeris datis and al-Khwarizmi's Algebra were common sources for those engaged in more advanced studies (i.e., they were not normally the subject of ordinary lectures, but were readily available to interested students, and would perhaps have been the subject of occasional extraordinary lectures). Euclid's Elements, supplemented by the commentaries of Pappus and Campanus, was the central text for geometry, and a number of medieval texts on practical and speculative geometry were in circulation as well. For astronomy, the Sphere of Sacrobosco and the Theorica planetarum were the most commonly used teaching texts, sometimes supplemented by al-Farghani's Elements of Astronomy (the subject of Regiomontanus's Padua lectures). Advanced students could read numerous more specific treatises by Arabic and Latin authors. For optics, the Perspectiva communis of John Peckham was the most common basic text, with texts... (shrink)

ArgumentThe aim of this paper is to employ the newly contextualized historiographical category of “premodern algebra” in order to revisit the arguably most controversial topic of the last decades in the field of Greek mathematics, namely the debate on “geometrical algebra.” Within this framework, we shift focus from the discrepancy among the views expressed in the debate to some of the historiographical assumptions and methodological approaches that the opposing sides shared. Moreover, by using a series of propositions related toElem.II.5 as (...) a case study, we discuss Euclid's geometrical proofs, the so-called “semi-algebraic” alternative demonstrations attributed to Heron of Alexandria, as well as the solutions given by Diophantus, al-Sulamī, and al-Khwārizmī to the corresponding numerical problem. This comparative analysis offers a new reading of Heron's practice, highlights the significance of contextualizing “premodern algebra,” and indicates that the origins of algebraic reasoning should be sought in the problem-solving practice, rather than in the theorem-proving tradition. (shrink)

In this book, best-selling author and mathematician Haim Shapira presents an introduction to mathematical theories which deal with the most beautiful concept ever invented by humankind: infinity. Written in clear, simple language and aimed at a lay audience, this book also offers some strategies that will allow readers to try their ability at solving truly fascinating mathematical problems. Infinity is a deeply counter-intuitive concept that has inspired many great thinkers. In this book we will meet many sages, both familiar and (...) unfamiliar: Zeno and Pythagoras, Georg Cantor and Bertrand Russell, Sofia Kovalevskaya and Emmy Noether, al-Khwarizmi and Euclid, Sophie Germain and Srinivasa Ramanujan. The world of infinity is inhabited by many paradoxes, and so is this book: Zeno paradoxes, Hilbert's "Infinity Hotel", Achilles and the gods paradox, the paradox of heaven and hell, the Ross-Littlewood paradox involving tennis balls, the Galileo paradox and many more. Aimed at the curious but non-technical reader, this book refrains from using any fearsome mathematical symbols. It uses only the most basic operations of mathematics: adding, subtracting, multiplication, division, powers and roots - that is all. But that doesn't mean that a bit of deep thinking won't be necessary and rewarding. Writing with humour and lightness of touch, Haim Shapira banishes the chalky pallor of the schoolroom and offers instead a truly thrilling intellectual journey. Fasten your seatbelt - we are going to Infinity, and beyond! (shrink)

Adriaan van Roomen published an outline of what he called a Mathesis Universalis in 1597. This earned him a well-deserved place in the history of early modern ideas about a universal mathematics which was intended to encompass both geometry and arithmetic and to provide general rules valid for operations involving numbers, geometrical magnitudes, and all other quantities amenable to measurement and calculation. ‘Mathesis Universalis’ (MU) became the most common (though not the only) term for mathematical theories developed with that aim. (...) At some time around 1600 van Roomen composed a new version of his MU, considerably different from the earlier one. This second version was never effectively published and it has not been discussed in detail in the secondary literature before. The text has, however, survived and the two versions are presented and compared in the present article. Sections 1–6 are about the first version of van Roomen’s MU the occasion of its publication (a controversy about Archimedes’ treatise on the circle, Sect. 2), its conceptual context (Sect. 3), its structure (with an overview of its definitions, axioms, and theorems) and its dependence on Clavius’ use of numbers in dealing with both rational and irrational ratios (Sect. 4), the geometrical interpretation of arithmetical operations multiplication and division (Sect. 5), and an analysis of its content in modern terms. In his second version of a MU van Roomen took algebra into account, inspired by Viète’s early treatises; he planned to publish it as part of a new edition of Al-Khwarizmi’s treatise on algebra (Sect. 7). Section 8 describes the conceptual background and the difficulties involved in the merging of algebra and geometry; Sect. 9 summarizes and analyzes the definitions, axioms and theorems of the second version, noting the differences with the first version and tracing the influence of Viète. Section 10 deals with the influence of van Roomen on later discussions of MU, and briefly sketches Descartes’ ideas about MU as expressed in the latter’s Regulae. (shrink)

Les documents chinois, depuis le Iersiècle, indiens, depuis le Vesiècle, et arabes, depuis le IXesiècle, contiennent des procédures tabulaires similaires pour l'extraction de racines carrées et cubiques avec des systèmes de numération positionnels. Par ailleurs tant Jia Xian, astronome chinois du XIesiècle, qu'al-Samaw'al, mathématicien arabe du XIIesiècle, ont extrait des racines de degré plus élevé par la procédure dite de Ruffini-Horner. L'article tente de définir une méthode textuelle pour organiser ce corpus, en y distinguant des axes pertinents qui permettent de (...) dégager similarités et différences, d'un point de vue tant historique que conceptuel. Une première partie analyse trois états différents des descriptions d'algorithmes entre le Iersiècle et le XIesiècle en Chine, qui présentent chacun une stabilité historique certaine. La réécriture qui fait passer d'un état au suivant laisse émerger progressivement une uniformité dans les composantes de l'algorithme, laquelle culmine avec des procédures du type Ruffini-Horner. Des critères textuels font apparaître une affinité plus grande de certains algorithmes, tels ceux décrits par Kūshyār ibn Labbān (ca1000), avec les textes chinois qu'avec les textes indiens, plus proches, eux, des algorithmes décrits par al-Khwārizmī. Des critères de même nature lient, d'une part, les algorithmes de Jia Xian et d'al-Samaw'al, d'autre part les algorithmes de Kūshyār et d'al-Samaw'al. (shrink)

The consumption of meat is a topic of concern because of its environmental and ethical implications. Consequently, plant-based meat alternatives have gained popularity. However, the consumption of these alternatives remains limited and understanding the factors that influence consumers’ intentions to consume them is vital. Current study aims to examine the crucial factors (i.e., knowledge of sustainable food production, problem awareness, outcome efficacy, descriptive social norms, injunctive social norms, and personal norms) that affect consumers’ intentions to consume plant-based meat alternatives, promoting (...) sustainable and ethical food choices. For this purpose, an online survey was conducted and data from 397 participants in China were analyzed using partial least squares structural equation modeling. The findings revealed that knowledge of sustainable food production, problem awareness, outcome efficacy, descriptive social norms, injunctive social norms, and personal norms had significant positive influences on the intention to consume plant-based meat alternatives. Findings can assist policymakers and practitioners in developing targeted strategies to promote sustainable and ethical food choices among consumers, such as improving their knowledge of sustainable food production, raising awareness of problems, promoting social norms, and fostering personal norms related to plant-based meat alternatives consumption. (shrink)

The Oxford Centre for Mission Studies has sought to provide holistic theological and missiological graduate education, particularly for Two-Thirds World church and academic leaders since 1983. This article addresses the question, ‘Has it succeeded?’ Originally presented at the 25th Anniversary of OCMS in 2008, this article looks back at the history behind its formation as well as assesses its accomplishments in the first 25 years. But there is value in such an exercise only if it serves the future; what issues (...) need to be addressed if OCMS is going to continues its impact in the next 25 years? This article looks back in order to forge ahead into the future with confidence and resolve. (shrink)

Each party in any given conflict has a role to play in the process of reconciliation. However, these respective roles are different depending on the power differential within the conflict. The role of the gospel peacemaker is to be aware of the power differential and to call each party to do their part toward reconciliation with one another. For those who have abused their power for self-gain at the expense of others need to repent. For those who have been victimized (...) by this power abuse need to forgive. And both abuser and abused need to lament. (shrink)

The reality of globalization warrants an understanding of mission that negotiates global and local realities. This article explores the way in which the global and the local have informed Mission as Transformation, a holistic missionary movement among radical evangelicals that developed in earnest since Lausanne ’74. How have local expressions — particularly Filipino expressions — of Transformation helped to form a global understanding of Transformation? And vice versa: How does a global understanding serve local expressions? The Transformational view of the (...) global-local — or glocal — relationship as symbiotic and not antagonistic undermines both universal theologies that are imposed on all cultures and to local theologies that lack global accountability. (shrink)