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I. Grattan-Guinness - Companion encyclopedia of the history and philosophy of the mathematical sciences, Volume 2

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Mathematics is one of the most basic -- and most ancient -- types of knowledge. Yet the details of its historical development remain obscure to all but a few specialists. The two-volume Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences recovers this mathematical heritage, bringing together many of the worlds leading historians of mathematics to examine the history and philosophy of the mathematical sciences in a cultural context, tracing their evolution from ancient times to the twentieth century.In 176 concise articles divided into twelve parts, contributors describe and analyze the variety of problems, theories, proofs, and techniques in all areas of pure and applied mathematics, including probability and statistics. This indispensable reference work demonstrates the continuing importance of mathematics and its use in physics, astronomy, engineering, computer science, philosophy, and the social sciences. Also addressed is the history of higher education in mathematics. Carefully illustrated, with annotated bibliographies of sources for each article, The Companion Encyclopedia is a valuable research tool for students and teachers in all branches of mathematics.Contents of Volume 1: -Ancient and Non-Western Traditions -The Western Middle Ages and the Renaissance -Calculus and Mathematical Analysis -Functions, Series, and Methods in Analysis -Logic, Set Theories, and the Foundations of Mathematics -Algebras and Number TheoryContents of Volume 2: -Geometries and Topology -Mechanics and Mechanical Engineering -Physics, Mathematical Physics, and Electrical Engineering -Probability, Statistics, and the Social Sciences -Higher Education andInstitutions -Mathematics and Culture -Select Bibliography, Chronology, Biographical Notes, and Index

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Cover

title Companion Encyclopedia of the History and Philosophy of the - photo 1
title:Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences. Volume 2
author:Grattan-Guinness, I.
publisher:Taylor & Francis Routledge
isbn10 | asin:
print isbn13:9780415037853
ebook isbn13:9780203014585
language:English
subjectMathematics--History, Mathematics--Philosophy, larpcal--Filosofia e fundamentos da matematica , larpcal--Matematica (historia)
publication date:1994
lcc:QA21.C645 1994eb
ddc:510/.9
subject:Mathematics--History, Mathematics--Philosophy, larpcal--Filosofia e fundamentos da matematica , larpcal--Matematica (historia)

Page i

Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences

Volume 2

Edited by
I.GRATTAN-GUINNESS

Companion encyclopedia of the history and philosophy of the mathematical sciences Volume 2 - image 2Companion encyclopedia of the history and philosophy of the mathematical sciences Volume 2 - image 3

LONDON AND NEW YORK

Page ii

First published in 1994

This edition published in the Taylor & Francis e-Library, 2003.

Simultaneously published in the USA and Canada
by Routledge Inc.
29 West 35th Street, New York, NY 10001

Selection and editorial matter
1994 I.Grattan-Guinness

The articles 1994 Routledge

All rights reserved. No part of this book may be reprinted or
reproduced or utilized in any form or by any electronic, mechanical
or other means, now known or hereafter invented, including
photocopying and recording, or in any information storage or
retrieval system, without permission in writing from the publishers.

British Library Cataloguing in Publication Data
A catalogue record for this book is available from the British Library

Library of Congress Cataloging-in-Publication Data
Companion encyclopedia of the history and philosophy of the mathematical
sciences/edited by Ivor Grattan-Guinness.
p. cm.
Includes bibliographical references and index.
ISBN 0-415-03785-9
1. MathematicsHistory. 2. MathematicsPhilosophy. I. Grattan
Guinness, I.
QA21.E57 1992
510'.9dc20 9213707
CIP

ISBN 0-203-01458-8 Master e-book ISBN

ISBN 0-203-32588-5 (OEB Format)

ISBN 0-415-03785-9 (set)
0-415-09238-8 (Vol. 1)
0-415-09239-6 (Vol. 2)

Illustration on title page:

Antelopes drawn by the (Ts)Chokwe people of Angola in their tradition
of monolinear art; the main block of the pattern is composed of one
continuous line, and is so designed that a regular lattice of dots can be
inserted in the spaces (see P.Gerdes, Lusona: Geometrical Recreations of
Africa, 1991, Maputo, Mozambique: Eduardo Mondlare University Press, 15).
On this tradition see 1.8 by C.Zaslavsky, Section 3.

Page iii

ADVISORY EDITORIAL BOARD

The late E.J.AITON (Manchester, England): mechanics and engineering

S.G.BRUSH (College Park, Maryland, USA): physics

J.FAUVEL (Milton Keynes, England): education and institutions

I.GRATTAN-GUINNESS (London, England): calculus and analysis; logic and foundations

J.J.GRAY (Milton Keynes, England): geometries

E.KNOBLOCH (Berlin, Germany): probability and statistics

A.C.LEWIS (Hamilton, Canada): bibliography and reference

A.G.MOLLAND (Aberdeen, Scotland): medieval and Renaissance periods

D.PINGREE (Providence, Rhode Island, USA): non-Western traditions

H.M.PYCIOR (Milwaukee, Wisconsin, USA): algebras

Page iv

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Page v

Contents
VOLUME 1

Part 0
Introduction

Part 1
Ancient and non-Western traditions

1.0

Introduction

1.1

Babylonian mathematicsJens Hyrup

1.2

Egyptian mathematicsC.S.Roero

1.3

Greek mathematics to AD 300Alexander Jones

1.4

Greek applied mathematicsAlexander Jones

1.5

Later Greek and Byzantine mathematicsAlexander Jones

1.6

Pure mathematics in Islamic civilizationJ.P.Hogendijk

1.7

Mathematics applied to aspects of religious ritual in IslamDavid A.King

1.8

Mathematics in Africa: Explicit and implicitC.Zaslavsky

1.9

Chinese mathematicsJ.C.Martzloff

1.10

Indigenous Japanese mathematics,Wasan Tamotsu Murata

1.11

Korean mathematicsYong Woon Kim

1.12

Indian mathematicsTakao Hayashi

1.13

Tibetan astronomy and mathematicsGeorge Gheverghese Joseph

1.14

Mathematics in medieval Hebrew LiteratureY.T.Langermann

1.15

Maya mathematicsM.P.Closs

1.16

The beginnings of counting and numberJohn N.Crossley

1.17

Some ancient solutions to the problem of fractioning numbersKarine Chemla

Part 2
The Western Middle Ages and the Renaissance

2.0

Introduction

2.1

Euclidean and Archimedean traditions in the Middle Ages and the RenaissanceJrgen G.Schnbeck

Page vi

2.2

Practical geometry in the Middle Ages and the RenaissanceH.lHuillier

2.3

The Coss tradition in algebraKarin Reich

2.4

Abbacus arithmeticW.Van Egmond

2.5

LogarithmsWolfgang Kaunzner

2.6

Medieval and Renaissance mechanicsA.G.Molland

2.7

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