Taming the unknown : history of algebra from antiquity to the early twentieth century PDF
Preview Taming the unknown : history of algebra from antiquity to the early twentieth century
2 3 4 TAMING THE UNKNOWN 5 TAMING THE UNKNOWN A History of Algebra from Antiquity to the Early Twentieth Century VICTOR J. KATZ AND KAREN HUNGER PARSHALL PRINCETON UNIVERSITY PRESS PRINCETON AND OXFORD 6 Copyright © 2014 by Princeton University Press Published by Princeton University Press, 41 William Street, Princeton, New Jersey 08540 In the United Kingdom: Princeton University Press, 6 Oxford Street, Woodstock, Oxfordshire, OX20 1TW Jacket images: Background images: Title page of Discours de la method by René Descartes, from the Plimpton Collection of the Rare Book and Manuscript Library, Columbia University. Problem on parabolas from Elementa curvarum linearum by Jan de Witt, in the 1659 edition of Descartes’s Geometria, from the David Eugen Smith Collection of the Rare Book and Manuscript Library, Columbia University. Mathematicians, left to right: Luca Pacioli, Pierre de Fermat, Évariste Galois, James Joseph Sylvester, Georg Frobenius, Emmy Noether. Detail portrait of the mathematician Luca Pacioli and an unknown young man by Jacopo de’Barbari. Museo Nazionale di Capodimonte, Naples, Italy. © Scala/Ministero per I Beno e le Attivitá culturali/Art Resources, NY. Image of Noether courtesy of Drs. Emiliana and Monica Noether. All Rights Reserved Library of Congress Cataloging-in-Publication Data Katz, Victor J. Taming the unknown: history of algebra from antiquity to the early twentieth century / Victor J. Katz and Karen Hunger Parshall. pages cm Includes bibliographical references and index. ISBN 978-0-691-14905-9 (hardcover: alk. paper) 1. Algebra–History. I. Parshall, Karen Hunger, 1955- II. Title. QA151.K38 2014 512–dc23 2013024074 7 British Library Cataloging-in-Publication Data is available This book has been composed in ITC New Baskerville Printed on acid-free paper. ∞ press.princeton.edu Typeset by S R Nova Pvt Ltd, Bangalore, India Printed in the United States of America 2 4 6 8 10 9 7 5 3 1 8 We dedicate this book to our spouses, PHYLLIS KATZ and BRIAN PARSHALL, and to our parents, BESS and MARTIN KATZ (in loving memory) and JEAN KAY “MIKE” and MAURICE HUNGER 9 Contents Acknowledgments xi 1 Prelude: What Is Algebra? 1 Why This Book? 3 Setting and Examining the Historical Parameters 4 The Task at Hand 10 2 Egypt and Mesopotamia 12 Proportions in Egypt 12 Geometrical Algebra in Mesopotamia 17 3 The Ancient Greek World 33 Geometrical Algebra in Euclid’s Elements and Data 34 10
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