In this unique insight into the history and philosophy of mathematics and science in the mediaeval Arab world, the eminent scholar Roshdi Rashed illuminates the various historical, textual and epistemic threads that underpinned the history of Arabic mathematical and scientific knowledge up to the seventeenth century. The first of five wide-ranging and comprehensive volumes, this book provides a detailed exploration of Arabic mathematics and sciences in the ninth and tenth centuries. Extensive and detailed analyses and annotations support a number of key Arabic texts, which are translated here into English for the first time. In this volume Rashed focuses on the traditions of celebrated polymaths from the ninth and tenth centuries 'School of Baghdad' - such as the Banu Musa, Thabit ibn Qurra, Ibrahim ibn Sinan, Abu Jafar al-Khazin, Abu Sahl Wayjan ibn Rustam al-Quhi - and eleventh-century Andalusian mathematicians like Abu al-Qasim ibn al-Samh, and al-Mu'taman ibn Hud. The Archimedean-Apollonian traditions of these polymaths are thematically explored to illustrate the historical and epistemological development of 'infinitesimal mathematics' as it became more clearly articulated in the eleventh-century influential legacy of al-Hasan ibn al-Haytham ('Alhazen'). Contributing to a more informed and balanced understanding of the internal currents of the history of mathematics and the exact sciences in Islam, and of its adaptive interpretation and assimilation in the European context, this fundamental text will appeal to historians of ideas, epistemologists, mathematicians at the most advanced levels of research.

Bringing together a broad range of contributors including art, architecture, and design academic theorists and historians, in addition to practicing artists, architects, and designers, this volume explores the place of the sketchbook in contemporary art and architecture. Drawing upon a diverse range of theories, practices, and reflections common to the contemporary conceptualisation of the sketchbook and its associated environments, it offers a dialogue in which the sketchbook can be understood as a pivotal working tool that contributes to the creative process and the formulation and production of visual ideas. Along with exploring the theoretical, philosophical, psychological, and curatorial implications of the sketchbook, the book addresses emergent digital practices by way of examining contemporary developments in sketchbook productions and pedagogical applications. Consequently, these more recent developments question the validity of the sketchbook as both an instrument of practice and creativity, and as an educational device. International in scope, it not only explores European intellectual and artistic traditions, but also intercultural and cross-cultural perspectives, including reviews of practices in Chinese artworks or Islamic calligraphy, and situational contexts that deal with historical examples, such as Roman art, or modern practices in geographical-cultural regions like Pakistan.

Bringing together a broad range of contributors including art, architecture, and design academic theorists and historians, in addition to practicing artists, architects, and designers, this volume explores the place of the sketchbook in contemporary art and architecture. Drawing upon a diverse range of theories, practices, and reflections common to the contemporary conceptualisation of the sketchbook and its associated environments, it offers a dialogue in which the sketchbook can be understood as a pivotal working tool that contributes to the creative process and the formulation and production of visual ideas. Along with exploring the theoretical, philosophical, psychological, and curatorial implications of the sketchbook, the book addresses emergent digital practices by way of examining contemporary developments in sketchbook productions and pedagogical applications. Consequently, these more recent developments question the validity of the sketchbook as both an instrument of practice and creativity, and as an educational device. International in scope, it not only explores European intellectual and artistic traditions, but also intercultural and cross-cultural perspectives, including reviews of practices in Chinese artworks or Islamic calligraphy, and situational contexts that deal with historical examples, such as Roman art, or modern practices in geographical-cultural regions like Pakistan.

In this unique insight into the history and philosophy of mathematics and science in the mediaeval Arab world, the eminent scholar Roshdi Rashed illuminates the various historical, textual and epistemic threads that underpinned the history of Arabic mathematical and scientific knowledge up to the seventeenth century. The first of five wide-ranging and comprehensive volumes, this book provides a detailed exploration of Arabic mathematics and sciences in the ninth and tenth centuries. Extensive and detailed analyses and annotations support a number of key Arabic texts, which are translated here into English for the first time. In this volume Rashed focuses on the traditions of celebrated polymaths from the ninth and tenth centuries 'School of Baghdad' - such as the Banu Musa, Thabit ibn Qurra, Ibrahim ibn Sinan, Abu Jafar al-Khazin, Abu Sahl Wayjan ibn Rustam al-Quhi - and eleventh-century Andalusian mathematicians like Abu al-Qasim ibn al-Samh, and al-Mu'taman ibn Hud. The Archimedean-Apollonian traditions of these polymaths are thematically explored to illustrate the historical and epistemological development of 'infinitesimal mathematics' as it became more clearly articulated in the eleventh-century influential legacy of al-Hasan ibn al-Haytham ('Alhazen'). Contributing to a more informed and balanced understanding of the internal currents of the history of mathematics and the exact sciences in Islam, and of its adaptive interpretation and assimilation in the European context, this fundamental text will appeal to historians of ideas, epistemologists, mathematicians at the most advanced levels of research.

Ikhwan al-Safa' (The Brethren of Purity) were the anonymous adepts of a tenth-century esoteric fraternity of lettered urbanites that was principally based in Basra and Baghdad. This brotherhood occupied a prominent station in the history of science and philosophy in Islam due to the wide reception and assimilation of their monumental encyclopedia: Rasa'il Ikhwan al-Safa' (The Epistles of the Brethren of Purity). This compendium contained fifty-two epistles that offered synoptic explications of the classical sciences and philosophies of the age. Divided into four classificatory parts, it treated themes in mathematics, logic, natural philosophy, psychology, metaphysics and theology, in addition to moral and didactic fables. The Ikhwan were learned compilers of scientific and philosophical knowledge, and their Rasa'il constituted a paradigmatic legacy in the canonization of philosophy and the sciences in mediaeval Islamic civilization.
This present volume gathers studies by leading philosophers, historians and scholars of Islamic Studies, who are also the editors and translators of the first Arabic critical editions and first complete annotated English translations of the Rasa'il Ikhwan al-Safa', which will be published in the OUP Series that this present volume initiates, as well as being members of the Editorial Board.
The chapters of this present volume explore the conceptual and historical aspects of the philosophical and scientific contents of the Rasa'il and their classification, as well as investigating the authorship and dating of this corpus and the impact that the Ikhwan's intellectual tradition exercised in the unfolding of the history of ideas in Islam.

The Ikhwan al-Safa' (Brethren of Purity), the anonymous adepts of a tenth-century esoteric fraternity based in Basra and Baghdad, hold an eminent position in the history of science and philosophy in Islam due to the wide reception and assimilation of their monumental encyclopaedia, the Rasa'il Ikhwan al-Safa' (Epistles of the Brethren of Purity). The fifty-two epistles offer synoptic accounts of the classical sciences of the age, treating themes in mathematics, logic, natural philosophy, psychology, metaphysics, and theology, in addition to didactic fables. The Rasa 'il constitutes a paradigmatic legacy in the canonization of philosophy and the sciences in mediaeval Islamic civilization, and has also shown a permeating influence in Western culture.
This volume is the fifth of the series, consisting of the first critical edition of the Rasa 'il in its original Arabic, complete with the fully annotated English translation. Prepared by Dr Nader El-Bizri, Epistles 1 and 2 (on arithmetic and geometry) present technical and epistemic analyses of mathematical concepts and their metaphysical underpinnings, in terms of investigating the properties of numbers and of geometric magnitudes, based primarily on the traditions of Nicomachus of Geresa and of Euclid as interpreted by the Ikhwan. With a Pythagorean construal of the ultimate principles of mathematics within the symbolic order of mysticism, and inspired by their own ontological outlook on the articles of faith in Islam, the Ikhwan view arithmetic and geometry through a monotheistic spiritual lens. This informed their treatment of mathematical knowledge, in pedagogic and heuristic terms, as part of the essential disciplines of the quadrivium, which aimed at preparing novices to study logic, then sciences of nature and the soul, before graduating to the lofty topics of theology and metaphysics. The volume also provides an overview of the mathematical sciences within the Islamic intellectual milieu, and of the tenth-century urban culture of Mesopotamian and Syrian locales.