Table Of ContentSCIENTIFIC PRACTICES AND
THE PORTUGUESE EXPANSION IN ASIA (1498-1759)
HISTORY OF
M T H E MTICAL 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
M TH E M TIC AL 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
'M
FUNDAQ~O
CALOUSrE CMAF CL
GULBENKIAN I
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-PublicationD ata
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 “Historyo f 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,a nd 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 181 9, 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 2 0c~en tury, due to the works of researchers such as Joaquim Bensaude (18 59-
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
from Portugal in 1759. The landing of Vasco da Gama in India in 1498
opened a new era in the relations between Europe and Asia, in particular
regarding the circulation of scientific knowledge. This led to major social
and intellectual changes in both continents. The Society of Jesus controlled
education in Portugal and in the Empire in the middle of the 16* century.
It was therefore central to the network of knowledge transmission until
the Society was expelled from Portugal in 1759.
There were three main themes for the Conference, which were described
as follows in the Conference’s program:
1. Pacing and Mapping the World - First and foremost, the newly
explored domain had to be mapped: the development of cartography,
the collection of astronomical observations, and of data relating to
nature and to societies encountered, resulted in a new picture of the
world. European maps began to use coordinates and different kinds
of mathematical projections. These transformed human-localised
space into a uniform system of reference. To Jesuit missionaries,
maps, which conveyed many Christian symbols, epitomised Western
experience. The encounter between this system and those used until
then in Asia sometimes resulted in interesting syntheses.
2. Transmission, Translation and Teaching - Translation into hitherto
unknown languages in many cases turned out to be a prerequisite to
teaching the Gospel and those aspects of European science that were
linked to it in the missionaries’ minds. The reception of these
elements of scientific knowledge by local elites can only be
understood in the light of local systems of learning. In the other
direction, it was knowledge about Asia rather than Asian knowledge
that was brought back to Europe. Although some transfers of
technology did occur, little of Asian learning and techniques was
deemed of interest by Europeans, including the Jesuits themselves.
