Studies in the History of Natural Sciences  NO.3 2010 

The Earliest Taosi Observatory and Its Possible Observing Years

LI Yong

(National Astronomical Observatories, Chinese Academy of Sciences, Beijing 100012, China)

Abstract　Taosi Observatory, possibly the earliest observatory possibly in the world, was found in 2005 in Taosi Town of Xiangfen City located in Shanxi Province. It has a sector structure and consists of one observing center and twelve observing slots. In order to investigate its essential conditions as a typical ancient observatory, and by referring to modern observations to imitate ancient works on this site, the contemporary astronomical system are employed to simulate the scheme when the sun just rose from behind the top of remote mountains between 3000 BC and 1000 BC. It is obtained that the possible observing years of this observatory were earlier than 1500 BC and ascertained that 1956 BC is the best year. There all 12 slots could observe 21 times in one tropical year and the average error is about 0°.11 for per slot and the biggest error is 0°.7. The mean errors are 4.5 days from the observing dates to their neighborhood solar terms. The purpose of the ancient observatory is ascertained to be more likely to survey and investigate the particular dates of Taosi culture which perhaps related to the original of afterwards 24 solar terms, or to provide the accurate times for sacrifice or other important events. But because of having neither the main buildings above the earth surface nor other known document information, it is hard to give detailed information or precise deductions.

Key words　astroarchaeology, Taosi town, observatory site, observing years

Research on the Structure of Moon-dial and Star-dial of Ming and Qing Dynasties

WANG Yumin

(Beijing Ancient Observatory, Beijing Planetarium, Beijing 100005, China)

Abstract 　On the base of collecting the records of almost all the documents and the　 cultural relic about moon-dial and star-dial, and also the base of using the works of our predecessors for reference, this article studies and analyzes the structure and usage of moon-dial and star-dial of Ming and Qing Dynasties. The main clue is to sort out their structures，and the secondary clue is to reproduce their models and observe with the models. The article also analyzes how the scales are divided, where the original points are and which directions they tend to.

Moon-dial can be divided into two types: the early type and the late type. Star-dial can also be divided into two types: the type of the fixed under-dial and the type of the both dials moving. The ways of the operation of the four types are different. When we observe with the models, we find that moon-dial have comparatively more errors but star-dial less. Furthermore, we find that some scales of the stone sun-moon-dial standing in front of the Yangxing Palace in the Forbidden City are not right. Finally, the article puts forward the suggestions of reproducing moon-dial and star-dial.　

Key words　moon-dial, star-dial, structure, early type, late type, reproduction

Geometrical Knowledge of Pre-Qin Period: A View Based on the Study of Mo Zi

ZOU Dahai

(Institute for the History of Natural Science, CAS, Beijing, 100190)

Abstract　The investigation on the geometrical knowledge of Pre-Qin China by making use of Mo Zi is significant not only for the study on the history of mathematics in early China but also for the understanding of the early stage of the forming of Chinese thought and culture. This paper analyzes the geometrical notions and knowledge in the relevant documents of Mo Zi, points out their range, nature and characteristics, and position in the system of Mohist knowledge. By comparing the results with relevant documents especially of the School of Logicians and ancient mathematics, the paper analyzes the geometrical knowledge of Pre-Qin China and its nature and characteristics, and shows that Chinese developed two interactive categories of geometrical knowledge: the geometrical algorithms focusing on practical problems, and the theoretical knowledge of geometry focusing on the concepts and their relations. The latter category provides a sample for us to study how ancient people developed abstract and theoretical geometry from empirical knowledge. The diversification of Pre-Qin mathematics, which is closely related to the Pre-Qin background of social revolution, ideology emancipation, contention of various schools of thought, is an important component part of the prosperity of Pre-Qin learning and thoughts.

Key words　Mo Zi, history of learning in Pre-Qin Period, geometrical knowledge of Pre-Qin Period, history of mathematics in China, School of Logicians

A Pythagorean Theorem Problem in Qin Bamboo Manuscripts on Mathematics, Shu, Collected by Yuelu Academy

XIAO Can, ZHU Hanmin

(Yuelu Academy, Hunan University, Changsha 410082, China)

Abstract　This article analyzes a problem in Qin bamboo manuscripts on mathematics, Shu, collected by the Yuelu Academy of Hunan University in Changsha. The problem is about how to calculate the diameter of a buried log. It is interesting that the same problem can be found in the Nine Chapters on Mathematical Procedures which is the most important of all ancient Chinese mathematical texts. After analysis, this problem is believed to be documentary evidence showing that the ancient Chinese were aware of a particular case of the Pythagorean Theorem. And the article speculates the mid-8th century BC to be the earliest date of this Pythagorean Theorem problem. But it still have doubts about the problem. It is also possibly associated with another mathematical principle, that corresponding sides of two similar right triangles are proportional.

Key words　Qin bamboo Manuscripts on Mathematics, Shu, the Pythagorean theorem

A New Research on Shushu jiuzhang

ZHENG Cheng, ZHU Yiwen

(Institute for the History of Natural Science, CAS, Beijing 100190, China)

Abstract　Qin Jiushao's Shushu jiuzhang (1247) is one of the most important works in the history of Chinese Mathematics. This article sorts out the textual history of the work, and reveals the special features of the manuscript copy by Zhao Qimei (1616) for the first time. It provides new materials and ideas for further study of Shushu jiuzhang in the context of rod calculus tradition.

Key words　Qin Jiushao, Shushu jiuzhang, edition, Zhao Qimei, rod calculus

Study on the Microstructure and Alloy Technology of Bronzes Excavated from the Ancient Jun District

LUO Wugan，

（Department of Scientific History and Archaeometry, Graduate University of the Chinese Academy of Sciences, 100049 Beijing, China；The Joint Laboratory of Human Evolution and Archaeometry, Beijing 100044, China）

QIN Ying，

（Laboratory of Archaeometry, University of Science and Technology of China, Hefei 230026, China）

HUANG Fengchun，

（Institution of Cultural Relics and Archaeology of Hubei Province, Wuhan 430077, China）

WANG Changsui

（Department of Scientific History and Archaeometry, Graduate University of the Chinese Academy of Sciences, 100049 Beijing, China；The Joint Laboratory of Human Evolution and Archaeometry, Beijing 100044, China）

Abstract　In this paper some bronzes, which were excavated from Qiaojiayuan tombs, are analyzed. From metallographic and XRF analyses, it is found that the conten of Pb is higher in bronze vessels, while another component Sn is lower. Some artifacts, such as sword, which needs high intensity and rigidity, contain few Pb, and some forged artifacts contain little Pb. The ancient blacksmith forged and did heat treatment on the bronze blade in order to improve its intensity and rigidity. The results indicate that, the alloy technology of these bronzes was at a higher level. And the blacksmith was profoundly cognizant of the law of alloy.

Key words　ancient Jun district，bronzes，alloy technology，Qiaojiayuan tombs

European Astrology in Early Qing China: Xue Fengzuo's and Smogulecki's Translation of Cardano's Commentaries on Ptolemy's Tetrabiblos

Nicolas Standaert

(Katholieke Universiteit Lenven)

Abstract　This article identifies and presents the Chinese translation of Girolamo Cardano's (1501—1576) Commentaries on Ptolemy's Treatise on Astrology， which contains Cardano's commentary on Ptolemy's (ca.100-ca.178) Tetrabiblos or Quadripartitum (Four Books), a systematic treatise on astrology. A selective translation was made by the Chinese scholar Xue Fengzuo 薛凤祚 (1599/1600—1680) and the Polish Jesuit Nikolaus Smogulecki (Mu Nige 穆尼阁; 1610—1656) and included in Tianbu zhenyuan 天步真原 (True Source of the Pacing of Heavens).