《七政推步》的数理研究

From the eighth to the fourteenth centuries, most of the advances in astronomy were achieved by scholars in the Middle East, North Africa, and Moorish Spain. This work crossed religious and ethnic boundaries, with contributions from, among others, Arabs, Iranians, and Turks, and from Muslims, Jews, and Christians. In particular, Islamic astronomers began to appreciate the inadequacies of the parameters used in the Almagest. This led to numerous attempts to improve on Ptolemy’s values so as to produce more accurate tables, and also a much greater interest in the theoretical aspects of Ptolemy’s geometrical schemes..From the thirteenth to the seventeenth centuries, Islamic astronomy, including astronomical tables, instruments, and astrological materials had been gradually introduced into China. In the Yuan Dynasty (1206-1368) the Arabs (they must, in fact, have been largely Persian and Central Asians) played a role in Chinese science and technology quiet similar to the Indians in the Tang Dynasty (618-907). Then the Persian astronomer, Jamāl al-Din ibn Muhammad al-Najjari (Zhamaluding), devised for Khubilai Khan in the year of 1267 a new calendar, the Wannian Li (the Calendar for the forever), which was afterwards lost, and in any case failed in competition with the Shoushi Li of Gou Shoujing (1231-1316), of which the Ming Calendar Datong Li, started in 1364, was but a modification. In the beginning of the Ming Dynasty (1368-1644), a Muslim (Huihui) Astronomical Bureau was set up in parallel with the ordinary Astronomical Bureau, to which, however, after a couple of years it became subordinate. In 1382, Tianwenshu (Astrology, Official Translation by the Imperial Edict of the Ming) consists of abundant data on positional astronomy, together with much astrological materials which were highly appreciated by the first Emperor of the Ming Dynasty. A great deal of computation must have need, however, for the solar and lunar eclipses, planetary conjunctions to the Muslim methods, supplemented and re-issued as the Qizheng Tuibu (Calculations of the Motions of the Seven Luminaries) by Bei Lin (1429-1490) in 1477, which had been used as reference calendar to Datong Li in the Ming Dynasty for more than 270 years and still played a critical role in the quarrel between Islamic and Jesuit astronomies in the beginning period of the Qing Dynasty (1644-1911)..Having based upon the historical research achievements by the scholars from the Ming Dynasty to now, the project aims to reveal the astronomical parameters, models and the formula for the 39 tables in Qizheng Tuibu, resumes the calculating program for the solar and lunar eclipses, and retrospect to the western astronomical theories which are directly related to Qizheng Tuibu. The mathematical research results of Qizheng Tuibu will be benefit to the further understanding and reviews on Qizheng Suan, Waibian (Outer Book on the Calculation of the Seven Luminaries), compiled by Korean astronomers in the first half of the fifteenth century and Huihui Lifa, volumes 7, 8, 9 of Calendars in Ming Shi (History of the Ming Dynasty), and establish one of the foundations for the development of the interweaving framework among Indian, Islamic, Jesuit and Chinese astronomies.

公元8世纪至14世纪，伊斯兰天文学继承了源自古希腊天文学体系的两大传统：一是数理天文学家所建立的数学天文学传统，二是自然哲学家所建立的宇宙学传统。其数理天文学传统则被系统地引入了我国元明期间《回回历法》的编制中。.依据关于中国古代数理天文学转轨与中国天文学近代化历程的最新研究成果，整体解析明代贝琳（1429—1490）所编纂的《七政推步》（1477年，七卷），重新界定其所应用的天文学常数；揭示太阳加减立成，太阴和土、木、火、金、水五星第一加减比敷立成和第二加减远近立成所依据的运动模型和计算公式；完整复原《七政推步》有关日食、月食、月五星凌犯的推步方法；通过展开回回历法数理研究，追溯西学理论源流，为勾勒中国近代数理天文学发展图景奠定坚实的基础。.发掘中世纪沿丝绸之路各国的数理天文学遗产，深入开展天文学传播交流的研究，对于探讨我国天文学在近代科学发展过程中的客观作用与历史地位具有重要意义。

研究项目基于中国和伊斯兰近代数理天文学的最新研究成果，对明代钦天监监副贝琳（1429—1482）重编的《七政推步》进行整体数理解析。通过解读术文和数表，界定其采用的天文学常数；“复原”太阳、太阴和五星运动的模型和公式，对相关表格进行校勘。开展回回天文学数理研究，发掘丝绸之路中国和伊斯兰世界的天文学遗产，有助于勾勒中国近代数理天文学发展图景、探讨其在中国科学发展过程中的客观作用与历史地位。. 项目取得的主要进展如下：. 一、根据《七政推步》“太阳行度”和“太阴经度”术文，确定《七政推步》太阳、太阴运动的天文学模型与托勒密模型存在源流关系，其中太阳、太阴运动模型的天文学常数不同于托勒密和已知的伊斯兰天文表。. 二、根据《七政推步》“五星经度”术文，运用“复原”公式检验了五大行星的“第一加减比敷立成”和“第二加减远近立成”；确定《七政推步》行星运动的天文模型遵循和发展了托勒密的理论，特别是太阴运动模型和行星运动模型之间存在一致性。《七政推步》外行星采用了与托勒密不同的偏心率和半径，内行星则部分使用了托勒密行星理论的常数。. 三、根据《七政推步》“五星纬度”术文，并结合《桑珠芬尼天文表》的五星纬度表，重新检验了其双变量的五星“南北纬度立成”；给出了拟合表值的倾斜角（i）和最大偏离角（jm）。. 四、明确《七政推步》回归年长度（365.24218750日）、128年31闰日的源流，首次揭示《七政推步》“第一加减比敷”、“第二加减远近”与清前中期三部历法（《西洋新法历书》、《康熙永年历法》和《御制历象考成》）行星运动理论中的“初均”、“中分”、“次均”和“较分”存在理论上的等价性。. 五、释读阿拉伯语《桑珠芬尼天文表》（法国国家图书馆藏Arabe 6040）和《回回历法立成表》（俄罗斯科学院远东手稿部藏C 2460）的术文和数表，确定了《七政推步》实际岁差，并根据三份“经纬时加减立成”初步构建回回天文学“甘肃（38°10′）—南京（32°）—北京（40°）”的传播路径。