Studies in the History of Natural Sciences  NO.1 2008 

The Debate on the Nature of Motion in the Middle Ages

ZHANG Butian

(Department of Philosophy, Peking University, Beijing 100871, China)

Abstract　This paper summarizes the main thread of the debate on the nature of motion in the middle ages, which includes a brief survey of Aristotle's doctrine of categories and the ontological status of motion, Averroes' two distinctions about motion, Albertus Magnus' new representation of this problem using forma fluens and fluxus formae, William of Ockham's extreme nominalistic view and Jean Buridan's objection to Ockham's view. The significance of understanding the nature of motion is also discussed.

Key words　nature of motion, category, forma fluens, fluxus formae

Dividing the History of Technology into Stages: Principle and Project

JIANG　Zhenhuan

(Journal of Harbin Institute of Technology, Harbin 150001, China)

Abstract　Study on the historical division of technology can disclose the stages of technical development, and also regulate the technical development. The historical division of technology should follow three principles: the inner logic of technical development;the innate regulation of technical development and variation; the stage character of human nature cognition and the level of social productivity. Some philosophers and historians have already put forward various division projects, which have certain meaning for describing the stages of technical development, but with obvious shortages. By statistical analysis of modern technology, it can be discovered that there is always a technology as having a leading function each time, that also represents the total development trend of technology in that time. The alternation of leading technology and its leading cluster reflect the revolution of a technical development stage, and taking this as a project of the historical division of technology, the regulation of technical development can be known.

Key words　history of technology, division for the history of technology into stages, principle for dividing the history of technology into stages, project for dividing the history of technology into stages, regularity of technical development

The Mathematical Structure of the Solar Equation Table in the Dayan Calendar and Its Method for Interpolation

WU Jiabi

(College of Humanities, Donghua University, Shanghai 200051， China)

Abstract　The solar equation table of the Dayan Calendar is a mathematical table of equally quartic difference, and it reflects Yi Xing's profound understanding about the solar motion. Yi Xing adjusts the spacing of interpolation to unequal spacing and considers that it serves a reduced-order function, so he can use the quadratic function to achieve the calculations of the quartic interpolation table. But Yi Xing only adopts the difference equation to approach an approximate computation and fails to complete the second and the third iterative computations; therefore, its precision of the computation is subjected to inaccuracy.

Key words　Dayan Calendar, solar equation table, difference equation, iterative method

Position of the Sun in Ancient Chinese Records of Solar Eclipse

MA Liping

(National Time Service Center, Chinese Academy of Sciences, Xi'an 710600, China)

Abstract　The measurements of solar positions in solar eclipse records in ancient China are analyzed. Such records in official historical documents are mainly found in those of Western Han, Eastern Han, Tang, Song and Qing dynasties. The solar positions in these records were obviously calculated beforehand or afterworlds. Some local chronicles of the Ming and the Qing dynasties traced back the past ones, but most of their real-time records are erroneous. An analysis by modern computation shows that the records of the Han Dynasties were computed according to uniform solar motion, while for those of the Tang Dynasty, an annual correction was added. The origins of records of the Western Han, Eastern Han and Tang dynasties are discussed by comparing with results calculated according to ancient calendars.

Key words　history of astronomy, solar eclipse, records of solar positions, calendar

Reviewing the Process of Liu Hui's Deducing the Circular Constant Through “Modifying by Ratio”

ZHU Yiwen

(Department for the History and Philosophy of Science, Shanghai Jiao Tong University, Shanghai 200240, China)

Abstract　Liu Hui's method for deducing the circular constant is recorded in his comments to Nine Chapters on the Mathematical Art. However, there exits a dispute about how Liuhui got the circular constant π=39271250 through “modifying by ratio”. Mikami Yoshio, Shen Kangshen, Li Jimin and Guo Shuchun all have their own explanations. This article reviews Liu Hui's comments and recovers the process of Liu Hui's deducing the circular constant π=39271250, and analyzes the cause of the difference among the scholars. The ariticle stands at the point that the process of π=39271250 created contains both mathematic principle and other factors, and finally gives a new explanation to the historical fact.

Key words　Nine Chapters on the Mathematical Art，ratio of the circumference of a circle to its dismeter, Liu Hui, modifying by ratio

Source and Influence of the Numerical Solution for High Degree Equation in Tongwen Suanzhi

PAN Yining

(Mathematics & Software Institute, Sichuan Normal University, Chengdu 610068, China)

Abstract　It is widely accepted that the Tongwen Suanzhi of Li Zhizao (1565—1630) is mostly a translated work and comes from the Epitome Arithmeticae Practicae (1583) of Christoph Clavius (1537—1612) and some traditional Chinese mathematical works. In fact, the Tongwen Suanzhi comes from much more Chinese and Western mathematical works, and Li Zhizao tried to integrate the Western mathematical knowledge into traditional Chinese mathematics in his book. Based on Chinese and Western sources, this paper points out that the numerical solution of high degree equation of the Tongwen Suanzhi comes from the Arithmetica Integra (1544) of Michael Stifel (1487—1567). The Chinese literati during the Ming-Qing period studied the method of the Tongwen Suanzhi, and tried to improve it.

Key words　Tongwen Suanzhi, Arithmetica Integra, Li Zhizao, Matteo Ricci, Michael Stifel, equation

Gibbs and His Vector Theory

SUN Qinghua, BAO Fangxun

(School of Mathematics and System Science, Shandong University, Jinan 250100, China)

Abstract　The vector theory is one of the important achievements of the domain of mathematics and physics in the second half of the 19th century. Based upon systematically analyzing the work of Gibbs, this paper discusses J. W. Gibbs' significant contributions to vector theory and the origin of his thoughts. The idea of quarternions is the base of vector theory which J. W. Gibbs created. Maxwell's gentle criticism and discriminating employment of quarternions methods probably did not go unnoticed by J. W. Gibbs, so the times were for J. W. Gibbs, who made the most important and key step by his insight and ingenuity, and created the modern vector analysis system. Successful application of vector theory in physics and astronomy enabled the theory to develop rapidly and spread widely.

Key words　J. W. Gibbs, vector, vector theory, quartenions

Research into the Influence of L.Bachelier's Theory of Speculation on Mathematics

YANG Jing,

（Department of Foundation Courses, Beijing Union University, Beijing 100101, China）

XU Chuansheng,

(Department of Mathematics, Linyi Normal University, Shandong Linyi 276005, China)

WANG Chaowang

（Department of Foundation Courses, Beijing Union University, Beijing 100101, China）

Abstract　L. Bachelier's dissertation Thorie de la Spculation contains many ideas and results about the stochastics process theory. But the opinions about the impact of his works in the history of mathematics has not reached an agreement as yet. Based on orginal materials and relevant studies, this paper concludes that L. Bachelier's work has a great impact on the development of mathematics, besides economics.

Key words　L. Bachelier, stochastics process theory, mathematical influence

An Exploration into the Cause of Formation for the Meteorological Catastrophe That Occurred at Wanggongchang, Beijing in the 6th Year of Ming Dynasty's Tianqi Reign Period

LIANG Guojian

(Feicheng Meteorology Bureau, Shandong Province, Feicheng 271600，China)

Abstract　This article tidies up and analyzes the historical records about the catastrophe which happened at Wanggongchang, Beijing on May 30, 1626, including the form of the disaster system and an analysis of the characteristics of the accompanying phenomenon.The catastrople is found to be a strong convection and small-scale weather system caused by the attack of a very strong tornado weather system.The proposition of a very strong tornado weather system readily solves all problems concerning low temperature,without fire and blowing away all clothing that have puzzled people for many years.

Key words　Tianqi reign period,catastrophe, natural enigma,tornado

On the Earliest Chinese Record of 1522 on Inoculation Against Smallpox and the Legends on Its Inventor

JIANG Sheng

(Institute of Religion, Science and Social Studies, Shandong University, Jinan 250100, China)

Abstract　Through the study of newly found materials, this paper reveals that the earliest record of artificial inoculation against smallpox in ancient China appeared in the year of 1522 in Zheng Shanfu's correspondence with his friend Ying Nanzhou found in Zheng's collection Shaogu ji, thus negating the conclusion of the Longqing Reign (1567—1572) made by many Chinese scholars, and the year of 1549 dated by Joseph Needham out of the study of Douzhen xinfa by Wan Quan. Based on a comparative study of newly found materials in some manuscripts including Guangbu tianhua shuo and other relevant classics, the paper checks up on the major logical elements that contribute to naming the inventor of inoculation against smallpox in different legend texts. It also explores the possible cultural drive that produced the very mistake of replacing Emperor Zhen with Emperor Ren, when Wang Dan, the Prime Minister at Emperor Zhen's time was introduced in the story on the origin of inoculation in Douzhen dinglun. Meanwhile, the paper proposes some questions that deserve further explorations.

Key words　inoculation against smallpox, Shaogu ji,Guangbu tianhua shuo