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Darrera modificació: 2016-08-06
Bases de dades: Sciència.cat
Rashed, Roshdi, Classical Mathematics from al-Khwārizmī to Descartes, Londres - Nova York, Routledge (Culture and civilisation in the Middle East, 44), 2015, xvi + 749 pp.
- Resum
- 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.
Contents:
-- Introduction: Problems of method
-- Part I: Algebra and arithmetic
- I. Algebra
* 1 Algebra and its unifying role
* 2 Algebra and linguistics: the beginnings of combinatorial analysis
* 3 The first classifications 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
- II. Arithmetic
* 1 Euclidean, neo-Pythagorean and Diophantine arithmetics: new methods in number theory
* 2 Algorithmic methods
* 3 Thābit ibn Qurra and amicable numbers
* 4 Fibonacci and Arabic mathematics
* 5 Fibonacci and the Latin extension of Arabic mathematics
* 6 Al-Yazdī and the equation [***]
* 7 Fermat and the modern beginnings of Diophantine analysis
-- Part II: Geometry
* 1 The Archimedians and the problems of infinitesimals
* 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 Thābit ibn Qurra on Euclid's fifth postulate
-- Part III: The 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
- Matèries
- Aritmètica i geometria
Matemàtica
Arabisme
Àrab
- Notes
- Informació de l'editor
Obra original: D'al-Khwārizmī à Descartes: études sur l'histoire des mathématiques classiques, París, Hermann, 2011, 795 pp.
A la presentació: "Classical Mathematics from al-Khwārizmī to Descartes includes two new chapters – one on the transmission of Greek heritage into Arabic and the other on Descartes's mathematics – that did not appear in the original French of D'al-Khwārizmī à Descartes. Conversely, I have omitted here the chapter on burning mirrors (‘Les miroirs ardents, anaclastique et dioptrique'), a subject to which I devoted an entire book, which is now available in English [Geometry and Dioptrics in Classical Islam, London, al-Furqān, 2005]".
- URL
- https://books.google.es/books?id=F_VTBAAAQBAJ&lpg=P ...
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