The Cambridge Companion to Newton Sir Isaac Newton (1642–1727) was one of the greatest scientists of all time, a thinker of extraordinary range and creativity who has left enduring legacies in mathematics and physics. While most famous for his Principia, his work on light and color, and his discovery of the calculus, Newton devoted much more time to research in chemistry and alchemy, and to studying prophecy, church history, and ancient chronology. This new edition of The Cambridge Companion to Newton provides authoritative introductions to these further dimensions of his endeavors as well as to many aspects of his physics and mathematics. It includes a revised bibliography, a new introduction, and six new chapters: three replacing previous chapters on Newton’s mathematics, his chemistry and alchemy, and the reception of his religious views; and three on entirely new subjects, namely his religion, his ancient chronology, and the treatment of continuous and discontinuous forces in his second law of motion. rob iliffe is Professor of History of Science at the University of Oxford. george e. smith is Professor of Philosophy at Tufts University. Other Volumes in The Series of Cambridge Companions AbelArd Edited by Jeffrey e. brOWer and KevIN GUIlfOy AdOrNO Edited by THOmAS HUHN ANcIeNT ScePTIcISm Edited by rIcHArd beTT ANSelm Edited by brIAN dAvIeS and brIAN lefTOW AqUINAS Edited by NOrmAN KreTzmANN and eleONOre STUmP ArAbIc PHIlOSOPHy Edited by PeTer AdAmSON and rIcHArd c. 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GIbSON Jr. rAWlS Edited by SAmUel freemAN reNAISSANce PHIlOSOPHy Edited by JAmeS HANKINS THOmAS reId Edited by TereNce cUNeO and reNé vAN WOUdeNberG rOUSSeAU Edited by PATrIcK rIley berTrANd rUSSell Edited by NIcHOlAS GrIffIN SArTre Edited by cHrISTINA HOWellS ScHOPeNHAUer Edited by cHrISTOPHer JANAWAy THe ScOTTISH eNlIGHTeNmeNT Edited by AlexANder brOAdIe AdAm SmITH Edited by KNUd HAAKONSSeN SOcrATeS Edited by dONAld mOrrISON SPINOzA Edited by dON GArreTT SPINOzA'S ‘eTHIcS’ Edited by OllI KOISTINeN THe STOIcS Edited by brAd INWOOd leO STrAUSS Edited by STeveN b. SmITH TOcqUevIlle Edited by cHeryl b. WelcH UTIlITArIANISm Edited by beN eGGleSTON and dAle mIller vIrTUe eTHIcS Edited by dANIel c. rUSSell WITTGeNSTeIN Edited by HANS SlUGA and dAvId STerN The Cambridge Companion to Newton SeCONd ediTiON edited by rOb IlIffe University of Oxford GeOrGe e. SmITH Tufts University University Printing House, cambridge cb2 8bS, United Kingdom cambridge University Press is part of the University of cambridge. It furthers the University’s mission by disseminating knowledge in the pursuit of education, learning and research at the highest international levels of excellence. www.cambridge.org Information on this title: www.cambridge.org/9781107601741 © cambridge University Press 2002, 2016 This publication is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of cambridge University Press. first edition first published 2002 Second edition first published 2016 Printed in the United Kingdom by clays, St Ives plc A catalog record for this publication is available from the British Library Library of Congress Cataloging in Publication data Names: Iliffe, rob, editor. | Smith, George e. (George edwin), 1938—editor. Title: The cambridge companion to Newton / edited by rob Iliffe and George e. Smith. description: Second edition. | cambridge : cambridge University Press, 2016.| Includes bibliographical references and index. Identifiers: lccN 2015040735 | ISbN 9781107601741 (pbk. : alk. paper) Subjects: lcSH: Newton, Isaac, 1642-1727. | Physics—europe—History—17th century. | Physics—europe—History—18th century. |Science—europe— History—17th century. | Science—europe—History—18th century. classification: lcc qc16.N7 c35 2016 | ddc 530.092—dc23 lc record available at http://lccn.loc.gov/2015040735 ISbN 978-1-107-01546-3 Hardback ISbN 978-1-107-60174-1 Paperback cambridge University Press has no responsibility for the persistence or accuracy of Urls for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate. Contents Page l ist of figures ix list of contributors xi Preface to the second edition xv Introduction 1 rob iliffe and george e. smith 1 Newton’s philosophical analysis of space and time 34 robert disalle 2 Newton’s concepts of force and mass, with notes on the laws of motion 61 i. bernard cohen 3 Instantaneous impulse and continuous force: the foundations of Newton’s Principia 93 bruce pourciau 4 The methodology of the Principia 187 george e. smith 5 Newton’s argument for universal gravitation 229 william harper 6 Newton and celestial mechanics 261 curtis wilson 7 Newton’s optics and atomism 289 alan e. shapiro vii viii contents 8 Newton’s metaphysics 321 howard stein 9 A brief introduction to the mathematical work of Isaac Newton 382 niccolò guicciardini 10 Newton, active powers, and the mechanical philosophy 421 alan gabbey 11 A preliminary reassessment of Newton’s alchemy 454 william r. newman 12 The religion of Isaac Newton 485 rob iliffe 13 Isaac Newton, historian 524 mordechai feingold 14 Newton and eighteenth-century christianity 554 scott mandelbrote 15 Newton and the leibniz–clarke correspondence 586 domenico bertoloni meli bibliography 597 Index 615 Figures 2.1 Newton’s parallelogram rule for motions produced by impul- sive forces. 71 2.2 The area law for uniform rectilinear motion. 76 2.3 Newton’s polygonal path (from the first edition of the Principia, 1687). 77 2.4 The trajectory of a moving body that has received a blow or has been struck by an impulsive force. 84 3.1 The figure illustrating lemma 7 in the Principia. 102 3.2 The moving deflection LQ⃗ measures the deviation from uni- form straight line motion. 106 3.3 The moving deflection LQ⃗ generated in a given time by an instantaneous impulse acting on a body at P. 110 3.4 Newton’s original figure and a redrawn version, illustrating the meaning of the second law, for the continuous force case. 117 3.5 Illustrating the compound Second law for a continuous force and an instantaneous impulse. 119 3.6 The figure that Huygens drew to illustrate his second and third hypotheses in the Horologium oscillatorium and the figure that Newton drew to illustrate his second law. 127 3.7 The redrawn figure that Huygens drew to illustrate the applica- tion of his three hypotheses to gravity acting in the direction of motion and the reproduced figure that Newton drew to illustrate the application of his first two laws to a force in the direction of motion. 127 3.8 The figure used in the Principia to illustrate corollary 1 of the laws. 130 3.9 The compound Second law applied to the motion of a body that describes a line under the influence of a force that remains parallel to that line. 133 ix