《授时历草》“立天元—求矢术”复原

RECURRENCE OF "THE METHOD OF FINDING SEGITTA BY SETTING TIAN YUAN YI" OF "THF DRAFT OF THE SHOUSHI CALENDAR

本文根据《梅氏丛书辑要》《赤水遗珍》(1761)中梅钰成关于“授时历立天元一求矢术”的记录,恢复了《授时历草》(1281)这一段珍贵史料,分析了它与李治、朱世杰所用天元术的异同之处,并且指出《授时历》作者是直接套用沈括会圆术,利用全弧背来推导出割圆求关术的。

This paper recuperates 'the method of finding segitta by setting Tian Yuan Yi' of 'the Draft of the Shoushi Calendar'(1281) according to a record in the Chishui Yizhen (Pearls recovered from the Red River) (1761) by Mei Juecheng. The paper shows the differences and similarities of this method from those of the Song and Yuan mathematicians, and points out that the method of finding sagitta by dividing circumference was directly derived from the Hui Yuan method by Shen Kuo.