关孝和对《授时历》中弧矢割圆术的研究

Seki Takakazu′s study on Hushigeyuanshu in the Shoushi Li

目的 廓清关孝和对《授时历》中求黄赤道差、黄赤内外差的几何算法的基本线索。方法 历史分析和文献考证。结果 详细分析了关孝和对《授时历》中"论黄赤道差"、"论黄赤内外差"和"论白道与黄赤道差"前两条的解释和图说。另外,关孝和根据传入日本的《天文大成管窥辑要》的原文顺利解决了第3条中的白道交周问题。结论 认为由于原文过于简单,所以关孝和的工作具有创造性。关孝和在17世纪前的日本是绝无仅有地完全弄懂了《管窥辑要》的一位学者。

AimTo clear up the main clue of Seki Takakazu′s geometrical calculation method on Lunhuangchidaocha and Lunhuangchineiwaicha in the Shoushi Li(A.D.1280).MethodsThe method of historical analysis and textual research of document are used to study the original works of Seki Takakagu.ResultsThe illustration and explanation made by Seki Takakazu about the above two problems involved in the Shoushi Li are studied.It is thought that Seki Takakazu had resolved Baidaojiaozhou on the basis of Guankuijiyao.ConclusionsBecause the original text of Guankuijiyao was very simple, Seki Takakazu′s work was of creativity. He was the only mathematician who fully understood Guankuijiyao in Japan before the 17th century.