SCIENTIFIC PRACTICES AND THE PORTUGUESE EXPANSION IN ASIA (1498-1759) HISTORY OF MTHEMTICAL S C I E NC E S: PORTUGAL AND EAST ASIA I1 University of Macau, China 10 - 12 October 1998 edited by LUIS SARAIVA University of Lisbon, Portugal 1: World Scientific NEW JERSEY * LONDON - SINGAPORE * BElJlNG * SHANGHAI HONG KONG * TAIPEI CHENNAI This page intentionally left blank SCIENTIFIC PRACTICES AND THE PORTUGUESE EXPANSION IN ASIA (1498-1759) HISTORY OF MTH E MTICAL S C I EN C E S: PORTUGAL AND EAST ASIA I1 Scientzfic Committee: Jean Dhombres (CNRS: Paris, France) Catherine Jami (CNRS: Paris, France) Liu Dun (Chinese Academy of Sciences: Beijing, China) Luis Saraiva (Coordinator of the Committee; CMAF: Lisbon, Portugal) Local Organizing Commiffee: Raymond Cheng (Chairman: FST; University of Macau: China) Isabel Loureiro (Co-Chairman: FST; University of Macau: China) Denise Sam (FST; University of Macau: China) Cower design: Claudia Hora, from a painting of Beijing Observatory, published in Revista de Culturn, 21, 1994, Instituto Cultural de Macau. Composition: Carlos Perpktuo FUNDAQ~O CALOUSrE CMAF CL GULBENKIAN I 'M This proceedings is made possible by a joint grant from the Calouste Gulbenkian Foundation, the Portuguese Society of Mathematics (SPM) and the Center for Mathematics and Fundamental Applications (CMAF). Published by World Scientific Publishing Co. Pte. Ltd. 5 Toh Tuck Link, Singapore 596224 USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601 UK ofice: 57 Shelton Street, Covent Garden, London WC2H 9HE British Library Cataloguing-in-PublicationData A catalogue record for this book is available from the British Library. HISTORY OF MATHEMATICAL SCIENCES: PORTUGAL AND EAST ASIA I1 - SCIENTIFIC PRACTICES AND THE PORTUGUESE EXPANSION IN ASIA (1498-1759) Copyright 0 2004 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher. For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher. ISBN 981-256-078-5 Printed in Singapore by World Scientific Printers (S) Pte Ltd ACKOWLEDGEMENTS We would like to express our gratitude to all who made this Conference, and the publication of its Proceedings, possible. First of all we would like to thank the speakers, for their talks, for their availability to do research on the themes of the Meeting, and for their commitment all the way through this process, from the early stages of preparation of the Meeting, to the interest and enthusiasm they showed during the Conference, and to the publication of these Proceedings. In particular, I wish to thank Professor Catherine JAMI, who played an essential part in shaping this Conference, and gave helpful comments for the revision of the papers. Secondly I would like to thank the organisers of the Meeting, the University of Macao and Centro de Matematica e Aplicaqbes Fundamentais, and all its sponsors: Ciimara Municipal das Ilhas, Comissiio Nacional para as Comemoraqbes dos Descobrimentos Portugueses, Direcqiio dos Serviqos de Turismo de Macau, Fundaqiio Macau, Fundaqiio Oriente, Instituto Cultural de Macau, Instituto de Cooperaqiio Cientifica e Tecnobgica Internacional, Instituto Politkcnico de Macau, Instituto Portugu& do Oriente, and Leal Senado de Macau, for making this Conference possible. I also wish to thank the Calouste Gulbenkian Foundation, an essential institutional reference concerning culture in Portugal, which is sponsoring the publication of the Proceedings, and Sociedade Portuguesa de Matematica, who made this sponsorship possible. Last, but not least, I want to thank the members of the local organising committee, chaired by Doctor Raymond CHENG, and the many scholars and students who helped the Conference to run so smoothly. Luis SARAIVA Centro de Matematica e Aplicaqbes Fundamentais / Universidade de Lisboa Lisbon, December 2001 This page intentionally left blank FOREWORD Luis SARAIVA CMAF, University of Lisbon The Conference “Historyof Mathematical Sciences: Portugal and East Asia I.” took place at the Faculty of Science and Technology of the University of Macao from the 10* to the 12* of October 1998. It was organised by the University of Macao and Centro de Matematica e Aplicaq6es Fundamentais, and was also sponsored by Ciimara Municipal das Ilhas, Comissiio Nacional para as Comemoraq6es dos Descobrimentos Portugueses, Direcqiio dos Serviqos de Turismo de Macau, Fundaqiio Macau, Fundaqiio Oriente, Instituto Cultural de Macau, Instituto de Cooperaqiio Cientifica e Tecnol6gica Internacional, Instituto PolitCcnico de Macau, Instituto PortuguQs do Oriente, and Leal Senado de Macau. The simple enumeration of these ten institutions makes clear the interest generated by the Conference and its theme, with the sponsorship coming from some of the most important institutions in Macao and Portugal. This event began the day after the end of the First Luso-Chinese Symposium on Nonlinear Evolution Equations and their Applications, a conference also organised by the University of Macao, which brought together thirty-five researchers, twenty-three from mainland China, three from Macao, and nine from Portugal. It was not a matter of chance that these two events happened in succession. This was done on purpose, firstly to point up the important relationship between practising a science and reflecting on its development, between the making of new knowledge and its critical integration into a historical setting, in short, between the past and the present. Secondly, it showed a willingness to have international collaboration and debate on mathematical issues of the present and the past, recognising that a major factor in the progress of society is the contact between different cultures, backgrounds, experiences, knowledge, ways of thinking and of acting. And thirdly, it clearly showed the University ... Vlll Luis SARAIVA of Macao’s willingness to promote this debate and to participate in it. It is fitting that this conference took place in Macao, a meeting point of East and West, a place always known for the coexistence of different cultures. The Conference “History of Mathematical Sciences: Portugal and East Asia 11” was intended to be a continuation of the debate started in 1995, at the Convent0 da Arrabida in Portugal, with the first Conference “History of Mathematical Sciences: Portugal and East Asia ” ’. The main aim of these conferences was to analyse the interaction between Europe and East Asia between the 16* and lS* centuries in the field of mathematical sciences, bringing to the fore the role of Portugal as an agent of transmission of European science to East Asia. The 1995 conference, organised by FundagBo Oriente, represented a real breakthrough, in the sense that its main purpose was the study of a theme until then almost completely ignored by Portuguese scholars. The relationship between Portugal and East Asia during the 16*, 17th,and 1S* centuries had been methodically studied by historians, including Portuguese researchers, in its economic, ideological, cultural, social, and political aspects. However there was a complete different picture when it came to the history of mathematical sciences: few scholars studied this subject, none of them Portuguese. Significantly, the four main histories of Portuguese mathematics (Gar950 Stockler’s in 1819, Rodolfo Guimariies’s in 1909, Pedro Jose da Cunha’s in 1929, and Francisco Gomes Teixeira’s in 1934) say hardly anything on the subject. Therefore, the Arrabida Meeting, with its three main themes (Mathematical Sciences and Arts: the meeting of East Asia and the European West; The Society of Jesus, agent of transmis- sion of European culture; Portugal and its Asian connections) and, equally as important, the emphasis on the absolute necessity of research done on primary sources (something which has been a recurrent shortcoming in the research work done by the majority of Portuguese researchers on the history of mathematics2), was an event that also aimed at stimulating serious research into Portuguese history of mathematics topics. The holding of this second Conference (and the publication of these Proceedings) also has a special meaning: it is an expression of the willingness to continue the debate started with the Arrhbida Meeting, The Proceedings of this Conference were published in 2000 by FundaGFio Oriente. 2 This remark does not concern the history of nautical sciences, which blossomed in the 20~century, due to the works of researchers such as Joaquim Bensaude (1859- 1952), Lucian0 Pereira da Silva (1864-1926), Abel Fontoura da Costa (1869-1934), Luis de Albuquerque (1917-1992), and others, and has a history of its own. Foreword ix the corroboration that there are both researchers interested in studying and exchanging views on these issues, and a public keen to know about them. It is now clear to us that there are conditions to organise periodic conferences on this general theme, exactly as the organisers of the First Conference intended, when the idea of these meetings initially took shape. The limiting dates chosen for this second Conference are the arrival of Vasco da Gama in India in 1498 and the expulsion of the Society of Jesus