【摘要】 一行在《大衍历》中修正行星的不均匀运动时,放弃了隋代及初唐历法中的五星入气加减差算法,首创表格形式的五星爻象历,并设计了与此相应的五星盈缩差算法。文章在前人研究基础上,通过详细解读《大衍历》术文,指出《大衍历》中五星爻象历相当于行星中心差表,进退变率相当于宋代历法中的五星盈缩差,二者之间的转化系数由一组常数"乘数"和"除数"决定。《五纪历》沿着《大衍历》的思路,大大简化了乘数和除数的设置,《宣明历》不再设乘数和除数,其五星平见加减历已演变为宋代五星盈缩历的雏形,由此勾勒出唐宋时期五星盈缩差算法演变的历史脉络。此外,文章还利用《大衍历》火星爻象历构造了火星盈缩历,并讨论了《大衍历》以后各历中火星盈缩历的精度。更多还原

【Abstract】 In Dayan Li,Yixing gave up the algorithm of wuxingruqijiajiancha used by calendar-makers in the Sui Dynasty and the early Tang Dynasty when he adjusted planetary equation of center and first used planetary Yaoxiangli in table form and designed the algorithm of expansion and contraction difference of Five Stars. Based on previous study and basic idea of planetary theory in Dayan Li,this paper points out that meanings of jintuibianlv of planetary theory in Dayan Li is equivalent to expansion-contraction-difference-algorithm of Five Stars in calendars of the Song Dynasty and the transformation coefficients between jintuiji and jintuibianlv is related to two constants chegnshu and chushu. Along this line of thought,Wuji Li made a few adjustments to chegnshu and chushu. Although Xuanming Li didn’t use chengshu and chushu any more,pingjianjiajianli in Xuanming Li was the antecedent of yinsuoli of the Song Dynasty. This paper constructs Mars’ s table of expansion and contraction difference according to yaoxiangli and discusses the precision of the table of expansion and contraction difference of Five Stars in some calendars after Dayan Li.更多还原