Japanese Mathematics in the Edo Period ( )

Transcription

1 Science Networks. Historical Studies 40 Japanese Mathematics in the Edo Period ( ) A study of the works of Seki Takakazu (?-1708) and Takebe Katahiro ( ) Bearbeitet von Annick Horiuchi, Silke Wimmer-Zagier 1st Edition Buch. xxvii, 350 S. Hardcover ISBN Format (B x L): 15,5 x 23,5 cm Gewicht: 839 g Weitere Fachgebiete > Mathematik > Mathematik Allgemein > Geschichte der Mathematik Zu Leseprobe schnell und portofrei erhältlich bei Die Online-Fachbuchhandlung beck-shop.de ist spezialisiert auf Fachbücher, insbesondere Recht, Steuern und Wirtschaft. Im Sortiment finden Sie alle Medien (Bücher, Zeitschriften, CDs, ebooks, etc.) aller Verlage. Ergänzt wird das Programm durch Services wie Neuerscheinungsdienst oder Zusammenstellungen von Büchern zu Sonderpreisen. Der Shop führt mehr als 8 Millionen Produkte.

2 Contents Acknowledgments XIII Preface to the English Edition XV Technical Notes XVII Preface XIX Part I The Beginnings of Wasan 1 Introduction 3 The Contribution of the Jesuits Mōri Shigeyoshi The Evolution of Mathematics in the 17th Century Notes

3 VI Contents 1 The Jinkōki (1627) by Yoshida Mitsuyoshi A Highly Successful Manual Yoshida Mitsuyoshi and the Suminokura The Jinkōki and the Suanfa tongzong The Arithmetic of the Jinkōki Conclusion Notes The Jugairoku (1639) by Imamura Tomoaki Presentation of the Author and of the Textbook Preface of the Jugairoku Analysis of the Textbook The Extraction of Square and Cube Roots in the Jugairoku The Study of Areas and Volumes in the Jugairoku Examples of Square and Solid Figures The New Figures Imamura and the Chinese Works Conclusion Notes The Sanso (1663) by Muramatsu Shigekiyo Presentation of the Author and of the Work The Problems Problem V-1, Chapter Dividing into Diminishing Parts Problem III-38, Chapter Excess and Deficit

4 Contents VII 3.3 Research on the Circle Presentation of the Problem The Method of Calculation Estimation of Areas and Volumes Introduction Geometric Techniques Techniques for Solving Equations Conclusion Notes The Treatise of Ancient and Modern Mathematics (1671) by Sawaguchi Kazuyuki The Author The Tianyuan Procedure The Statements The Use of Counting Rods The Procedures The Place of the Tianyuan Procedure in the Treatise of Ancient and Modern Mathematics The 150 Problems of the Sanpō Kongenki The Solutions of the Problems The Fifteen Problems of Sawaguchi Notes Part II Seki Takakazu, His Time and His Mathematical Works 95 5 Seki Takakazu (? 1708) and His Time The Intellectual Context

5 VIII Contents 5.2 The Government of the Shōgun Tsunayoshi ( ) Cultural Contacts with Foreign Countries The Scientific Activities of the Jesuits in China The Calendar in Japan Seki Shinsuke Takakazu (? 1708) Seki Takakazu s Career as Retainer of the Bakufu Seki s Scientific Activities The Government of Ienobu ( ) Arai Hakuseki Takebe Katahiro ( ) The Life of Takebe Katahiro Katahiro s Career Takebe s Scientific Activities during the Period Conclusion Notes The Works of Seki Takakazu on Techniques for Solving Problems The Hatsubi Sanpō (Mathematical Treatise Revealing the Hidden Meaning) The Solution of the Fifteen Problems of Sawaguchi Reception of the Hatsubi Sanpō by Seki s Contemporaries The Endan of the Hatsubi Sanpō The Meaning of the Term Endan in the Hatsubi Sanpō Conclusion The Monographs on Problem Solving Methods Method for Solving Concealed Problems Seki s Contribution The Three Monographs Seki s Theory of Equations The Algorithm for Extracting Roots Rectification of the Formulation of Problems Multiplicity of the Roots of an Equation

6 Contents IX The Problem of the Existence of Roots Replacement of Coefficients: Method for Eliminating the Linear Term Methods for Correcting Faulty Problems The Configurations of Extraction A Work by Takebe? The Section The Ten Quotients of the Accomplished Classic of Mathematics Conclusion Notes Part III Takebe Katahiro, Mathematician and Advisor of the Shōgun 201 Introduction 203 Notes The Career of Takebe Katahiro as Advisor of the Shōgun Takebe as Cartographer Maps of the Provinces (kuniezu) in the 17th Century The Realization of the Global Map by Yoshimune Takebe s Concept of Cartography Takebe s Sources of Inspiration Takebe as Advisor in Astronomy The Calendar in Yoshimune s Time Nishikawa Joken ( ) The Lifting of the Ban: The Official Explanations The Lisuan Quanshu and the Xiyang Lijing The Preface of the Lisuan Quanshu The Activities of Nakane and Takebe during the Years The Years and the Failure of Yoshimune s Calendar Reform Conclusion Notes

7 X Contents 8 Takebe s Works on Trigonometry Introduction Takebe s Mathematical Work of the Second Period Trigonometry in the Work of Takebe Katahiro On the Genesis of the Idea of an Inexhaustible Procedure of the Arc The Question of the Chinese Heritage The Problems of the Circle and the Arc in Seki s Katsuyō Sanpō The Accomplished Classic of Mathematics or the Transitional Stage The Inexhaustible Procedure of the Tetsujutsu Sankei Mathematical Research According to Takebe Katahiro The Notion of Tetsujutsu Research by Means of the Principle Research by Means of Numbers The Object of Mathematical Research: The Laws of Nature Conclusion Application to Calendrical Science Chronology Approximations to the Values of the Arc and the Sagitta An Alternative to the General Procedures: Repeated Foldings Takebe s Trigonometric Tables Conclusion A New Way of Finding the Procedure of the Arc Mikami s Researches Summary of the Method of the Enri Kohaijutsu Analysis of the Method Infinite Series in China at the Beginning of the 18th Century Comparison with Newton s Approach to the Binomial Formula Conclusion Notes

8 Contents XI Conclusion 313 Notes Bibliography 317 Abbreviations Preliminary Remarks A. Chinese and Japanese Books before Meiji B. Chinese and Japanese Books and Journal Articles since Meiji. 326 C. Books and Journal Articles in Western Languages Glossary 349 List of Figures with Indication of Sources 359 Index 363