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mathematics and the laws of nature Revised Edition
Math Chapter Title iii
the history of
mathematics and the laws of nature developing the language of science Revised Edition
John Tabak, Ph.D.
MATHEMATICS AND THE LAWS OF NATURE: Developing the Language of Science, Revised Edition Copyright © 2011, 2004 by John Tabak, Ph.D. All rights reserved. No part of this book may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording, or by any information storage or retrieval systems, without permission in writing from the publisher. For information contact: Facts On File, Inc. An imprint of Infobase Learning 132 West 31st Street New York NY 10001 Library of Congress Cataloging-in-Publication Data Tabak, John. Mathematics and the laws of nature : developing the language of science / John Tabak—Rev. ed. p. cm.—(The history of mathematics) Includes bibliographical references and index. ISBN 978-0-8160-7943-8 (alk. paper) ISBN 978-1-4381-3624-0 (e-book) 1. Mathematics—History. 2. Science—History. I. Title. QA21.T22 2011 510.9—dc22 2010021599 Facts On File books are available at special discounts when purchased in bulk quantities for businesses, associations, institutions, or sales promotions. Please call our Special Sales Department in New York at (212) 967-8800 or (800) 322-8755. You can find Facts On File on the World Wide Web at http://www.infobaselearning.com Excerpts included herewith have been reprinted by permission of the copyright holders; the author has made every effort to contact copyright holders. The publisher will be glad to rectify, in future editions, any errors or omissions brought to its notice. Text design by David Strelecky Composition by Hermitage Publishing Services Illustrations by Dale Williams Photo research by Elizabeth H. Oakes Cover printed by Yurchak Printing, Inc., Landisville, Pa. Book printed and bound by Yurchak Printing, Inc., Landisville, Pa. Date printed: May 2011 Printed in the United States of America 10 9 8 7 6 5 4 3 2 1 This book is printed on acid-free paper.
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To George Baker. He is a law unto himself.
contents
Preface Acknowledgments Introduction
1 The Preliminaries Mathematics versus Science and Engineering The Mesopotamians The Ancient Sky Recording the Stars to Predict the Future The Astronomical Calculations The Tablets
2 Mathematics and Science in Ancient Greece Ratios and the Measure of the Universe A Geometry of the Universe A Rotating Earth Archimedes: Fusing Physics with Mathematics The Law of the Lever
3 A Period of Transition Nicholas Oresme Nicolaus Copernicus Johannes Kepler Platonic Solids Leonardo da Vinci and the Equation of Continuity Proving Leonardo’s Equation of Continuity
x xvi xvii
1 1 7 8 12 15 18
20 20 27 31 32 35
39 40 42 48 53 55 59
4 New Sciences
61
Simon Stevin
63
Stevin and Music Galileo Galilei Fermat, Descartes, and Wallis
66 70 74
5 Mathematics and the Law of Conservation of Momentum
83
The Laws of Motion The Discovery of Neptune Limits on the Applicability of Newton’s Laws
88 93 97
6 Mathematics and the Law of Conservation of Mass
102
Leonhard Euler and the Science of Fluid Dynamics The Mathematics of Combustion Limits on the Applicability of Conservation of Mass
107 109 110
7 Mathematics and the Laws of Thermodynamics
114
A Failed Conservation Law Sadi Carnot Calculating the Efficiency of a Carnot Engine James Prescott Joule The First Law of Thermodynamics The Second Law of Thermodynamics Entropy Models and Reality
114 120 126 128 130 135 141 142
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