Studies in the History of Natural Sciences 　NO.1 2006

Planetary Theory in Ancient China　  QU Anjing

Abstract　The aim of planetary theory in traditional Chinese astronomical mathematics is to calculate the true geocentric longitude at arbitrary given time. The theory consists of two parts: (1)Making use of an astronomical table in a synodic period and interpolation, the mean geocentric longitude of a planet will be determined. This step is permitted under such a hypothesis that both the planet and the Earth are in mean motion around the Sun. (2) Making use of a function to calculate the deviation between the true and mean geocentric longitudes of the planet. For analyzing the precision of traditional Chinese algorithm for the mean geocentric longitude of planet, its theoretical model is established by the author. Taking Mars in the Jiyuan Li (1106) as an example, the result shows that the average error of its mean geocentric longitude in a synodic period is about 4'. According to its theoretical model of the true geocentric longitude, the astronomical meaning of planetary theory in ancient China is revealed. Its evolution, in brief, could be described as follows: Before the phenomena of irregular movement of the Earth's and planet's revolution were discovered by Zhang Zixin in around 550, only its mean geocentric longitude of planet was calculated by calendar-makers. From Liu Zhuo's Huangji Li (600) to Yixing's Dayan Li (724), an algorithm for the deviation between the true and mean longitude of planet was put to use. This deviation was supposed to be caused by the equation of center of planet only. Based on the method of Liu Zhuo and Yixing, a new algorithm was developed by Bian Gang in his Chongxuan Li (892). It incorporated the equation of center of the Earth in the deviation between the true and mean geocentric longitudes. After the Jiyuan Li (1106), no substantial changes were made on the planetary theory in traditional Chinese mathematical astronomy.

Key words　planet, mathematical astronomy, China, longitude

Working Out an Educational System (Part on Mathematical Education in Japanese Primary Schools) from the Perspective of Cultural History　　　 Wuyunqiqige

Abstract　This paper attempts to reexamine the creation of a new educational system, especially the adoption of the teaching of Western arithmetic, the abandonment of Wasan teaching, and the revival of abacus calculating. It points out that: (1) The thesis of Ogura Kinnosuke (小金之助）that at the beginning of the new educational system, Wasan (traditional Japanese mathematics) rather than Western arithmetic was once adopted to be taught in the mathematical classrooms of primary schools in Japan, is wrong; (2) The original edition of the new educational system could not be considered to have been suited to the real atmosphere of the early Meiji Japanese society, but it expressed the hope of the leaders of the educational reform; and (3) “The so-called revival of abacus calculating” has its deep roots in the cultural soil of East Asia, and it should be understood that people in the early Meiji period calculated with abacus when needed in their ordinary life. So that is why abacus calculating might revive with the new guide of Western mathematical principles.

Key words　educational system, adoption of Western arithmetic, abandonment of Wasan, revival of abacus calculating

Election of the First Batch of Academicians of Academia Sinica in 1948　　 GUO Jinhai

Abstract　This paper throws light on the first election of academicians of Academia Sinica in 1948, gives the main reasons for the success of the election and its significance for modern scientific institutitionalization in China. Furthermore, it also briefs the background of the election decided by the Second Advisory Council of Academia Sinica, analyzes how regulations for the election were laid down and its contents, and explores the nomination of candidates for academicians and the appraisal of their competence. The paper points out that the essential reasons for the success of the election include: Chinese scientific circles had tended to become mature and already had large numbers of elite；the Second Advisory Council and the Preparatory Committee of the first election of academicians of Academia Sinica made an effective institutional arragement; most members of the Council complied with scientific criterions, attached importance to academic standards, and adhered to the democratic principle all through the election. The election is an apotheosis of electing elite completely chaired by modern Chinese intellectuals. The first election of academicians of Academia Sinica is an important symbol that modern scientific institutionalization in China began to enter a period of maturity.

Key words　Academia Sinica, first batch of academicians, election, Second Advisory Council, scientific institutitionalization

A Study on Two Earliest Translations of Western Anatomy　　　　　　　  NIU Yahua

Abstract　 Taixi Renshen Shuogai(Outline of Human Body of the West)and Renshen Tushuo (Illustrated Explanation of the Human Body)，translated by the Jesuits in the 17th century，are two earliest Chinese translations of Western anatomy.It was mostly considered in academic circles that the two Chinese translations introduced the old Galenical anatomy,and the knowledge of anatonmy introduced in the late Ming Dynasty was that in medieval Europe. However，by textual research and comparison between the two Chinese translations and The Fabric of Andreas Vesalius (1514～1564)，the author finds that the two translations reflect the anatomic system of Vesalius. The knowledge of anatomy introduced in the late Ming Dynasty is actually that flourished in Europe in the 16th century.

Key words　anatomy, Chinese translations， Joannes Terrenz， Jacobus Rho， Andreas Vesalius

The Rudiments of the Idea of Riemann for Geometry　　　　 DENG Mingli,　　 YAN Chenguang

Abstract　Based upon studying its relationships with other subjects, this paper points out three origins of the idea of Riemann for geometry:mathematics, physics and philosophy．The geometry in the first half of 19th century had a direct influence on Riemann's thinking．The research of physics, especially grand unifield theories, was also Riemann's interest．That made him study manifolds by infinitesimal analysis and review the foundation of space geometry．Herbart's study in philosophy was the source of inspiration for Riemann's knowledge about space, and probably led to the concept of manifold．The paper points out finally that the study of the idea of Riemann for geometry should be considered thoroughly．

Key words　 Riemann，geometrical thought，physics，philosophy，history of mathematics

Discussion on Sanxing Idea in Ancient Chinese Geography　　　　　　　 LI Hui

Abstract　This paper gives the thought of San Xings,which expatiates respectively on the conceptions of superior geographical conditions,topographical features,and the practice of geography,and points out the relationships among themThen it takes Feng Shui for an example to explain its application in the ancient geography of China

Key words　superior geographical conditions,topographical features,practice of geography,thought of San Xings,Feng Shui

Ancient Chinese Calendars in the Mathematical Perspective: An Essay Review of Qu Anjing's The Chinese Calendar and Mathematics　  SUN Xiaochun

Abstract　This article reviews Qu Anjing's The Chinese Calendar and Mathematics (Science Press, 2005). It points out that the book is mainly concerned with the reconstruction of astronomical constants and mathematical operations used in the making of calendars in ancient China. The book presents original studies and convincing conclusions and arguments on various important mathematical problems in calendar-making, such as the determination of Grand Epoch, the approximation of fractions, the method of interpolation, and the formularization of calendrical computations. The article concludes that this book, with remarkable achievements, is a stimulating work of interdisciplinary research of Chinese mathematical astronomy.

Key words　mathematical history, Chinese mathematics, ancient Chinese calendars, mathematical astronomy