Algebra - Sets, Symbols, and the Language of Thought (History of Mathematics) - Tabak John (2004).pdf

文档介绍：algebra
sets, symbols, and the
language of thought
THE HISTORY OF
MATHEMATICS
THE HISTORY OF
algebra
sets, symbols, and the
language of thought
John Tabak, .
ALGEBRA: Sets, Symbols, and the Language of Thought
Copyright © 2004 by John Tabak, .
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All rights reserved. No part of this book may be reproduced or utilized in any form or
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information storage or retrieval systems, without permission in writing from the pub-
lisher. For information contact:
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Library of Congress Cataloging-in-Publication Data
Tabak, John.
Algebra : sets, symbols, and the language of thought / John Tabak.
p. cm. —(History of mathematics)
Includes bibliographical references and index.
ISBN 0-8160-4954-8 (hardcover)
1. Algebra—History. I. Title.
2004
512—dc222003017338
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Text design by David Strelecky
Cover design by Kelly Parr
Illustrations by Sholto Ainslie
Printed in the United States of America
MP FOF 10 9 8 7 6 5 4 3 2 1
This book is printed on acid-free paper.
To Diane Haber, teacher, mathematician, and inspirator.
CONTENTS
Introduction: Algebra as Language xi
1 The First Algebras 1
Mesopotamia: The Beginnings of Algebra 2
Mesopotamians and Second-Degree Equations 5
The Mesopotamians and Indeterminate Equations 7
Clay Tablets and Electronic Calculators 8
Egyptian Algebra 10
Chinese Algebra 12
Rhetorical Algebra 16
2 Greek Algebra 18
The Discovery of the Pythagoreans 19
The mensurability of √224
Geometric Algebra 25
Al