The Good Life In The Scientific Revolution: Descartes, Pascal, Leibniz, And The Cultivation Of Virtue

The Good Life in the Scientific Revolution Descartes, Pascal, Leibniz, and the Cultivation of Virtue MAT THEW L. JONES THE GOOD LIFE IN THE SCIENTIFIC REVOLUTION The Good Life in the Scientific Revolution DESCARTES, PASCAL, LEIBNIZ, AND THE CULTIVATION OF VIRTUE Matthew L. Jones The University of Chicago Press Chicago & London Matthew L. Jones is associate professor of history at Columbia University. The University of Chicago Press, Chicago 60637 The University of Chicago Press, Ltd., London  C 2006 by The University of Chicago All rights reserved. Published 2006 Printed in the United States of America 15 14 13 12 11 10 09 08 07 06 5 4 3 2 1 ISBN-13 (cloth): 978-0-226-40954-2 ISBN-13 (paper): 978-0-226-40955-9 ISBN-10 (cloth): 0-226-40954-6 ISBN-10 (paper): 0-226-40955-4 Library of Congress Cataloging-in-Publication Data Jones, Matthew L. (Matthew Laurence), 1972– The good life in the scientific revolution : Descartes, Pascal, Leibniz, and the cultivation of virtue / Matthew L. Jones. p. cm. Includes bibliographical references and index. ISBN 0-226-40954-6 (cloth : alk. paper)—ISBN 0-226-40955-4 (pbk. : alk. paper) 1. Science—History—17th century. 2. Mathematics—Philosophy—History—17th century. 3. Descartes, Ren´e, 1596–1650. 4. Pascal, Blaise, 1623–1662. 5. Leibniz, Gottfried Wilhelm, Freiherr von, 1646–1716. 6. Science–Moral and ethical aspects. I. Title. Q125.2.J66 2006 509.032—dc22 2006040491 ∞ The paper used in this publication meets the minimum requirements of the  American National Standard for Information Sciences—Permanence of Paper for Printed Library Materials, ANSI Z39.48-1992. This book is printed on acid-free paper. For Liz Contents List of Illustrations Acknowledgments List of Abbreviations A Note on Conventions Introduction ix xi xv xvii 1 PA R T 1 : D E S C A R T E S 1 Geometry as Spiritual Exercise 2 A Rhetorical History of Truth 15 55 PA R T 2 : PA S C A L 3 Mathematical Liaisons 4 The Anthropology of Disproportion 89 131 PA R T 3 : L E I B N I Z 5 Forms of Expression 6 Seeing All at Once 169 229 Epilogue 267 Notes Bibliography Index 271 329 363 Illustrations 1.1 1.2 1.3 1.4 1.5 3.1 3.2 3.3 3.4 3.5 5.1 5.2 5.3 5.4 5.5 Example problem Geometric machine and associated curve Descartes’ compass Quadratrix The problem of Apollonius Arithmetical triangle First three triangular numbers: 1, 3, 6 First three pyramidal numbers: 1, 4, 10 Figurate number table Quadrature of parabola Perspectival intuition behind Leibniz’s quadrature Transmutation of circle Characteristic triangle Example anamorphoses Method for the creation of the fresco Saint Jean l’Evang´eliste a` Patmos in anamorphosis ¨ 5.6 Title page of volume 1 of Georg Philipp Harsdorffer and Daniel Schwenter, Deliciae physico-mathematicae, oder Mathematische und philosophische Erquickstunden 5.7 Dance of the shadows 5.8 Pantograph 5.9 Dividing a curve 5.10 Instrument for making perspectival views 6.1 Schematic of Leibniz’s experiment on the collision of bodies 6.2 Leibniz’s 1686 conservation of force argument 23 24 29 40 41 97 99 99 100 115 171 172 173 181 182 185 188 197 201 209 241 262 Acknowledgments Concerning those authors who speak of their works as “my book,” “my commentary,” “my story,” and so forth, Mr. Pascal said that they seem like well-established burghers, always with a chez moi at their lips. This excellent man added that they would do far better to say: “our book,” “our commentary,” “our history,” and so forth, since usually more of what is good in such works comes from others than from themselves. M. de Vigneul-Marville, M´elanges de litt´erature