Cover

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pp. 1-7

Contents

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pp. vii-viii

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1. Introduction

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pp. 1-32

This book takes as its starting point an observation that one might hope would be uncontroversial: “civilizations” are no less imagined than “nations.” During the later decades of the twentieth century, the term “imagined communities” gained considerable prominence through critical studies of various forms of nationalism. ...

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2. Science as the Measure of Civilizations

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pp. 33-50

Imagining “civilizations” to be the central actors in historical drama, writers since the eighteenth century have devised a variety of defining features that were supposed to distinguish between them. Terms such as “modernity,” “science,” and “capitalism” headed the list of mutually incongruous candidates invoked to portray stark differences: ...

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3. From Copula to Incommensurable Worlds

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pp. 51-76

By adopting certain naive presuppositions, studies of the asserted problems encountered in translations between languages have often reached dramatic conclusions about the fundamental differences between civilizations. These presuppositions are naive in the sense that they circumvent many of the questions that should properly confront historical inquiry, ...

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4. Mathematical Texts in Historical Context

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pp. 77-130

The Song (960–1276) and early Yuan (1260–1368) mark the apex that traditional Chinese mathematics never again attained, the received historiography has maintained: during the period from the mid-Yuan until the arrival of the Jesuits at the end of the Ming dynasty (1368–1644), Chinese mathematical treatises were lost, ...

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5. Tracing Practices Purloined by the Three Pillars

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pp. 131-194

“Tattered sandals,” regrettably, was all that remained of Chinese mathematics, which could just as well be discarded because Western mathematics was in every respect superior—or at least so claimed Xu Guangqi (1562–1633) in his preface to the Guide to Calculation in the Unified Script (Tong wen suan zhi, 1613).1 ...

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6. Xu Guangqi, Grand Guardian

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pp. 195-256

Xu Guangqi (1562–1633) rose from presented scholar (jin shi) to one of the more distinguished positions in the official bureaucracy of the Ming dynasty, Grand Guardian of the Heir Apparent and Grand Secretary of the Hall of Literary Profundity (Taizi taibao, Wenyuange da xueshi). ...

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7. Conclusions

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pp. 257-264

Previous accounts of the “first encounter” of “China” and “the West” concur for the most part in their retelling of the historical events. In these accounts, China during the Ming dynasty (1368–1644), and especially during the later years of the Ming, is often held to have been in a period of profound decline ...

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Acknowledgments

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pp. 265-270

During the period in which this book was written, I have been fortunate to have benefited from the generous support of several institutions and the encouragement of numerous colleagues; I would thus like to express my gratitude for all their help. ...

Appendix A: Zhu Zaiyu’s New Theory of Calculation

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pp. 271-278

Appendix B: Xu Guangqi’s Right Triangles, Meanings

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pp. 279-290

Appendix C: Xu Guangqi’s Writings

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pp. 291-304

Bibliography

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pp. 305-366

Index

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pp. 367-374