History of Mathematical Sciences

ACKNOWLEDGMENTS

FOREWORD

CONTENTS

ABOUT THE AUTHORS

PICTURE OF CONFERENCE PARTICIPANTS

In the first history of Portuguese mathematics, Ensaio histórico sobre a origem e progressos das mathematicas em Portugal, the first history of mathematics in a single country published in Western Europe, written by the important Portuguese mathematician Francisco de Borja Garção Stockler (1759–1829) and published in Paris in 1819, the control of the Society of Jesus over public education was pointed out as one of the two major factors of the so called decline period of the Portuguese mathematics, the other one being the establishment of the Inquisition in Portugal. This period lasted roughly two hundred years, marked by the death of king D. João III in 1557 and the beginning of the reign of the king D. José in 1750.

Since then, and up to the 1940s, this view was maintained unchallenged. Starting with a paper by Pedro José da Cunha in 1940, and fully developed in the last 30 years, a new way of looking both to the 1580–1772 period and to the mathematics work of the Society of Jesus has been done.

In this paper it is analyzed the way Portuguese historians of mathematics up to 1940 have given account of this so called “decline” period, and how they saw the Society of Jesus and their mathematicians in this period. Besides the pioneering work of Stockler, we will consider Francisco do Castro Freire's Memória Histórica da Faculdade de Mathematica (1872); Rodolfo Guimarães's Les Mathématiques en Portugal (1909); Pedro José da Cunha's Bosquejo histórico das matemáticas em Portugal (1929), A Astronomia, a Náutica e as Sciências Afins (1929) and As Matemáticas em Portugal no Século XVII (1940); and Francisco Gomes Teixeira's História das Matemáticas em Portugal (1934).

No abstract received.

Among the products of Jesuit missionary activities during the “the Christian century” in Japan (1549–1650), a latin treatise called De sphaera deserves special attention. Sources show that it was composed by a Spanish Jesuit Pedro Gomez (1533–1600) in 1593, and used as a textbook by Japanese and European students preparing for the priesthood at Jesuit colleges in Japan.

This textbook played a significant role in the introduction of European cosmology into Japan, as it was the origin, or at least one of the sources, of several Japanese books, all of which were composed around the mid-seventeenth century. These books were similar in content, but differed in title and some other peculiars. They include:

(1)Nigi ryakusetsu (A brief discussion on the celestial and terrestial worlds)

(2)Kenkon bensetsu (A discussion on the heavens and the earth with critical commentaries)

(3)Nanban unkiron (A discussion by “Southern Barbarians” on yun-qi)

(4)Tenmon biyô (Compendium for astronomy)

They occupy a place of special significance, since they were the first full-scale presentation of Western physical sciences in Japan.

This paper does not aim to describe the relationship between these works, nor the intellectual impact which they had upon the history of Japanese cosmology. This has been done many times, mainly by Japanese scholars, though much still remains to be investigated. Rather, the focus here is on (1) the content and characteristics of De sphaera, and (2) how many manuscripts of the Japanese works exist today. Strange as it may seem, these aspects have received little meticulous consideration, with the result that the historical and textual background of each work has often been understood and described in rather vague terms. Obviously, what follows is more of an introduction than an exhaustive account of the results of my research.

Manuel Dias' (1574–1659) Tianwenlüe (Epitome of Questions on the Heavens, 1615) is a summary of European cosmographical and astronomical knowledge. It is a text in the tradition of commentaries on Sacrobosco's Sphere but with several important novelties. It is structured as a series of questions and answers, the questions being formulated by a Chinese and the answers given by an European. Also worth noting is the fact that it presents examples and data specifically adapted or calculated for China. But, above all, it is remarkable because it presents for the first time in Chinese a description of Galileo's telescopic observations.

Despite being frequently mentioned by historians of science, this text was never studied in detail and nearly every question related to it — composition, contents, diffusion, reception, etc. — remains to be clarified. In this paper I investigate the background of the composition of this text describing the scientific tradition where it stems from, namely, De sphaera literature in Portugal and in Jesuit schools in the sixteenth and early seventeenth century and, more specifically, Jesuit's presentation of Western science in China. The questions that will be treated here are mostly related to the author of the Tianwenlüe, his biography, his scientific competence and the sources he used to prepare the text. One question of direct relevance to the composition of the Tianwenlüe will be inspected in more detail: the spreading of news related to Galileo's discoveries among Jesuits in the Portuguese Assistancy. Finally, some words will be said on the impact of the book.

This article will not present any exciting, sensational new findings on the brief astronomical treatise entitled Tianwenlüe composed by the Portuguese Jesuit Manuel Dias Jr. (1574–1659), also known as Yang Manuo, in 1615, the 43^rd year of the Wanli period. Rather, it will recapitulate the textual history of Manuel Dias' Explicatio Sphaerae coelestis — as the Tianwenlüe is sometimes called in Latin —, thus contributing to the “reconnaissance” phase of a project, the final goal of which is to accomplish an annotated English translation of this short, yet very influential, treatise. Mainly, this article deals with the following editions of the Tianwenlüe: 1. Editio princeps; 2. Tianxue chuhan (First Collectanea of Heavenly Studies); 3. Qinding gujin tushu jicheng (Imperially approved Synthesis of books and illustrations past and present); 4. Siku quanshu (Complete Library of the Four Treasuries); and 5. Yihai zhuchen (Dust of Pearls from the Ocean of Arts). Of all these versions, the least satisfying in terms of editing is the one included in the Complete Library. By taking this inferior edition as its text of departure, the article tries to assess the different versions of the Tianwenlüe, specifically in terms of completeness and reliability.

No abstract received.

No abstract received.

No abstract received.

No abstract received.