Classical Mathematics from Al-Khwarizmi to Descartes

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Routledge, Aug 21, 2014 - History - 758 pages

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.


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between epistemology and history
The transmission of Greek heritage into Arabic
the fifth book of Apolloniuss
The founding acts and main contours of Arabic mathematics
Fermat and algebraic geometry
the beginnings of combinatorial analysis
The first classifications of curves
Thābit ibn Qurra and amicable numbers
Fibonacci and Arabic mathematics
Fibonacci and the Latin extension of Arabic mathematics
AlYazdī and the equation
Fermat and the modern beginnings of Diophantine analysis
The Archimedeans and problems with infinitesimals
The traditions of the Conics and the beginning of research
The continuous drawing of conic curves and the classification

Simplicius On the Euclidean definition of the straight line
Descartess ovals
Descartes and the infinitely small
Algorithmic methods
Algebra and its unifying role
Thābit ibn Qurra on Euclids fifth postulate
The celestial kinematics of Ibn alHaytham
From the geometry of the gaze to the mathematics of
The philosophy of mathematics

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About the author (2014)

Roshdi Rashed is one of the most eminent authorities on Arabic mathematics and the exact sciences. A historian and philosopher of mathematics and science and a highly celebrated epistemologist, he is currently Emeritus Research Director (distinguished class) at the Centre National de la Recherche Scientifique (CNRS) in Paris, and is the former Director of the Centre for History of Medieval Science and Philosophy at the University of Paris (Denis Diderot, Paris VII). He also holds an Honorary Professorship at the University of Tokyo and an Emeritus Professorship at the University of Mansourah in Egypt.

Michael H. Shank is professor of the History of Science at the University of Wisconsin-Madison, were he teaches surveys of the history of science from antiquity to Newton. His research interests focus on, and often stray beyond, the late-medieval Viennese astronomical and natural philosophical traditions.

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