中国唐宋时期五星盈缩差算法的演变轨迹——从爻象历到盈缩历

发布时间：2018-06-14 17:41

本文选题：大衍历 + 爻象历　；参考：《科学技术哲学研究》2016年02期

【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。
[Abstract]:When one row corrects the inhomogeneous motion of the planets in the Great derivative Calendar, it gives up the algorithm of adding and subtracting the five stars in the calendar of the Sui Dynasty and the early Tang Dynasty, and creates the five-star line image calendar in the form of the tabular form, and designs the corresponding algorithm of the five-star surplus and contraction. On the basis of previous studies, this paper points out that the five star line ephemeris in the Great Yan Calendar is equivalent to the planetary center difference table, and the rate of advance and regression is equivalent to the five star surplus and contraction difference in the Song Dynasty calendar. The conversion coefficient between the two is determined by a set of constant "multipliers" and "divisors". The addition and subtraction of the five stars has evolved into the embryonic form of the five star surplus and contraction calendar in the Song Dynasty, which outlines the historical context of the evolution of the five star shrinkage algorithm in the Tang and Song dynasties. In addition, the Martian surplus contraction calendar is constructed by using the Martian line image calendar, and the accuracy of the Martian retractive ephemeris in the later calendars is discussed.
【作者单位】：咸阳师范学院数学与信息科学学院;
【基金】：国家自然科学基金(11073016) 国家社会科学基金重大项目(15ZDB029) 教育部人文社会科学研究西部和边疆地区项目(14XJA770001) 陕西省社会科学基金(2014H04) 陕西省教育厅科学研究项目(14JK1795)
【分类号】：P194

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