关孝和《天文数学杂著》初探

A Primary Inquiry into Seki Takakazu's Miscellaneous Memoranda on Astronomy and Mathematics

对关孝和《天文数学杂著》中的天文历算工作进行较为全面的研究 ,特别指出了“《授时历》求五星定合定积定星校正图解”中的“改正术”与《授时历经》记载大致相同 ;“日景实测”中的“独特算法”与和算中求圆周率术和求弧背术有密切联系 ;《元史》中已论及盈缩和迟疾二种不均匀改正 ,并且《元史》中所述内容包括了关孝和定交日和交定度算法的改正术。图解是关氏历算工作的精华。关孝和亲自观测和校验 ,以其独特的视角 ,融合中国古代的数理天文方法 ,进一步完善了《授时历》的历算工作 ,有的还有所超越 ,在日本开辟出新的研究领域。

This paper first studies Seki Takakazu' s Miscellaneous Memoranda on Astronomy and Mathematics. Th e records of eclipse in the Spring and Autumn Period and Cizhenzhiceyan are analyzed. The paper draws a correct inference to Seki's u nique calculation pocess in his Rijingshice and reaches a conclu sion that the works of Seki Takakazu were based on his own observation.The proc ess is connected with Seki Takakazu's Kyu Enshuritsu Jutsu and Kyu Kohai Jutsu in Wasan. Some notes on eclipse and man y graphs are studied. The paper attaches great importance to Seki's graphs for eclipse . In a word, Seki's studies of the Shous hi Calendar opened up a new research field. Moreover, some of his studie s surpass those of Chinese scholars of the corresponding period. A series of Sek i's works on mathematical astronomy stood for the level of traditional Lisuan in Japan.