Rāshid, Rushdī, author.
New York, NY : Routledge/Taylor & Francis Group, 2015.
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Part of the series Culture and civilization in the Middle East 44;Culture and civilisation in the Middle East 44.
Notes:
- Includes bibliographical references and index.
- This book follows the development of classical mathematics and the relation between work done in the Arab and Islamic worlds and that undertaken by the likes of Descartes and Fermat. ‘Early modern,’ mathematics is a term widely used to refer to the mathematics which developed in the West during the sixteenth and seventeenth century. For many historians and philosophers this is the watershed which marks a radical departure from ‘classical mathematics,’ to more modern mathematics heralding the arrival of algebra, geometrical algebra, and the mathematics of the continuous. In this book, Roshdi Rashed demonstrates that ‘early modern,’ mathematics is actually far more composite than previously assumed, with each branch having different traceable origins which span the millennium. Going back to the beginning of these parts, the aim of this book is to identify the concepts and practices of key figures in their development, thereby presenting a fuller reality of these mathematics. This book will be of interest to students and scholars specialising in Islamic science and mathematics, as well as to those with an interest in the more general history of science and mathematics and the transmission of ideas and culture — Provided by publisher.
- Introduction: Problems of method: 1. The history of science: between epistemology and history — 2. The transmissions of Greek heritage into Arabic — 3. Reading ancient mathematical texts: the fifth book of Apollonius’s Conics — 4. The founding acts and main contours of Arabic mathematics Part I. I. Algebra. 1. Algebra and its unifying role — 2. Algebra and linguistics: the beginnings of combinatorical analysis — 3. The first classification of curves — 4. Descartes’s Géométrie and the distinction between geometrical and mechanical curves — 5. Descartes’s ovals — 6. Descartes and the infinitely small — 7. Fermat and algebraic geometry Part II. Arithmetic. 1. Euclidean, neo-Pythagorean and Diophantine arithmetics: new methods in number theory — 2. Algorithmic methods — 3. Thäbit ibn Qurra and amicable numbers — 4. Fibonacci and Arabic mathematics — 5. Fibonacci and the Latin extension of Arabic mathematics — 6. Al-Yazdï and the equation — 7. Fermat and the modern beginnings of Diophantine analysis Part II: Geometry. 1. The Archimedeans and problems with infiniteimals — 2. The traditions of the Conics and the beginning of research on projections — 3. The continuous drawing of conic curves and the classification of curves — 4. Thä ibn Qurra on Euclid’s fifth postulate Part III. Application of mathematics: astronomy and optics. 1. The celestial kinematics of Ibn al-Haytham — 2. From the geometry of the gaze to the mathematics of the phenomena of light — Conclusion: The philosophy of mathematics.
Subjects:
Requested by Haines, M. & Bloomberg, M.