关孝和对《授时历》中白道交周问题的研究  

Seki Takakazu′s research on problem of Baidao Jiaozhou in Shoushi Calender

作　　者：冯立升[1] 王海林[2] 

机构地区：[1]清华大学科学技术史暨古文献研究所,北京100084 [2]空军雷达学院基础课部,湖北武汉430019

出　　处：《陕西师范大学学报（自然科学版）》2004年第3期4-6,11,共4页Journal of Shaanxi Normal University：Natural Science Edition

基　　金：国家自然科学基金资助项目(10271051);吴文俊数学与天文学丝路基金资助项目(WSF20003-05)

摘　　要：白道交周算法被认为是《授时历》的五项创新方法之一,但中国明清时期的历算家已不能通晓该法.清初梅文鼎(1633—1721年)等所撰《明史·历志》曾详论前四项,但缺乏对白道交周问题的说明.清初黄宗羲(1610—1695年)虽大致复原了白道交周算法,但对某些细节没有弄清,推导过程还出现一处明显的错误.日本数学家关孝和(1640?—1708年)研究《授时历》的著作《授时发明》对白道交周法却有详细的讨论,他的相关工作有助于澄清过去研究这一问题存在的疑问.《授时历》中白道交周问题的算法,以天元术推导多项式方程,而明末清初天元术等宋元数学方法在中国失传,因而当时的历算家无法完全掌握推导过程.由于关孝和等日本数学家通过学习传入日本的元代数学著作掌握了天元术等数学方法,因而能够对《授时历》算法的每一细节作出说明.The algorithm of Baidao Jiaozhou, used to calculate the distance between two crossover Points along the equator, ecliptic and Moon′s path, was considered one of the five innovative methods in Shoushi Calendar, with which the Chinese mathematicians of the Ming and Qing Dynasty could no longer make acquainted. Mei Wending of the early Qing Dynasty have dissertated about four methods in detail, without explaining to the algorithm of Baidao Jiaozhou, there were still some specifics lacking of clarity, furthermore, a mistake could be easily found in his deductive process. However, The algorithm of Baidao Jiaozhou was dissertated detailed in Shoushi Faming by Seki Takakazu(1640—1708), a Japanese mathematician, in his research of Shoushi Calendar. Seki′s works helped to answer several doubts of the problem. In order to deduct polynomial equations in the algorithm of Baidao Jiaozhou in Shoushi Calendar, Tianyuan method was used, which had been lost in the early Qing Dynasty, resulting in the poor mastery of the whole deductive process by the contemporary Chinese mathematicians. Whereas, Seki and other Japanese mathematicians mastered mathematical methods such as Tianyuan method in their learning to the introductive mathematical works of the Yuan Dynasty, thus capable of explaining each specific of the algorithm in Shoushi Calendar.

关 键 词：关孝和 《授时历》 代数学 多项式方程 数学家 算法 数学方法 推导过程 疑问 细节 

分 类 号：N09[自然科学总论—科学技术哲学] O11[理学—数学]