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Distributed for Center for the Study of Language and Information

Ancient and Medieval Traditions in the Exact Sciences

Essays in Memory of Wilbur Knorr

This volume of essays is dedicated to Wilbur Knorr, an outstanding historian of science whose career was cut short much too early. Inspired by Knorr’s work, this volume concentrates on the history of ancient mathematics, the associated mathematical sciences, and their medieval and modern tradition.

This volume emulates the quality and diverse interests of Knorr’s innovative, exact, and far-reaching research. Topics inspired by Knorr include a study of geometric analysis and synthesis in ancient Greece and medieval Islam; examination of Eudoxus as originator for the ideas of proportionality underlying Book V of "Euclid’s Elements"; and the extent that Renaissance theorists of linear perspective had access to ancient sources. This book considers the status of Eudoxus’s theory of homocentric spheres in Greek astronomy and the examination of the status of in Greek mathematics. A detailed discussion of the geometrical chemistry of Plato’s Timaeus and its interpretation in antiquity stems from Knorr’s work, and a study of Plato’s concept of numbers and its relation to the Theory of Forms. Knorr’s varied interests motivate investigation into the representation of numbers in the Latin middle ages, or why we read Arabic numbers backwards, and the history of science in a chronology of the three dynasties in ancient China.

Table of Contents

Preface
Patrick Suppes, Julius M. Moravcsik & Henry Mendell
The Role and Development of Geometric Analysis and Synthesis in Ancient Greece and Medieval islam
J. L. Berggren & Glen Van Brummelen
Eudoxus: Parapegmata and Proportionality
David Fowler
Pappus’ Notes to Euclid’s Optics
Alexander Jones
The Trouble with Eudoxus
Henry Mendall
Why Did Greek Mathematicians Publish Their Analyses?
Reviel Netz
Plato’s Geometrical Chemistry and Its Exegesis in Antiquity
Ian Mueller
Plato on Numbers and Mathematics
Julius M. Moravcsik
Why We Read Arabic Numberals Backwards
Charles Burnett
The Chronology of the Three Dynasties
David S. Nivison
 

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