Imagined Civilizations This page intentionally left blank Roger Hart Imagined Civilizations China, the West, and Th eir First Encounter Th e Johns Hopkins University Press Baltimore © 2013 Th e Johns Hopkins University Press All rights reserved. Published 2013 Printed in the United States of America on acid-free paper 9 8 7 6 5 4 3 2 1 Th e Johns Hopkins University Press 2715 North Charles Street Baltimore, Maryland 21218-4363 www.press.jhu.edu Library of Congress Control Number: 2010924546 ISBN 13: 978-1-4214-0606-0 ISBN 10: 1-4214-0606-3 A catalog record for this book is available from the British Library. Special discounts are available for bulk purchases of this book. For more information, please contact Special Sales at 410-516-6936 or [email protected]. Th e Johns Hopkins University Press uses environmentally friendly book materials, including recycled text paper that is composed of at least 30 percent post-consumer waste, whenever possible. With enormous gratitude to all my teachers, with special thanks to Benjamin Elman a nd Mario Biagioli This page intentionally left blank Contents 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2 Science as the Measure of Civilizations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3 From Copula to Incommensurable Worlds . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 4 Mathematical Texts in Historical Context. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 5 Tracing Practices Purloined by the T hree Pillars . . . . . . . . . . . . . . . . . . . . . . . 131 6 Xu Guangqi, Grand Guardian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195 7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257 Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265 Appendix A: Zhu Zaiyu’s New Theory of Calculation . . . . . . . . . . . . . . . . . . . . . . . . 271 Appendix B: Xu Guangqi’s Right Triangles, Meanings . . . . . . . . . . . . . . . . . . . . . . . 279 Appendix C: Xu Guangqi’s Writings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 367 vii This page intentionally left blank Imagined Civilizations