一个被忽视的文本:胡适、朱载予的插补新方法

IF 0.7 2区 哲学 Q2 HISTORY & PHILOSOPHY OF SCIENCE
Gang Li, Anjing Qu
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引用次数: 0

摘要

本文对朱载堉(1536-1611)历法中一个被忽视的重要原始文本进行了翻译和解释。郭守敬的《历法》(1231-1316)的发明与应用,是历法体系构建理念的重大变革。在本文中,我们认为,通过给出仙虎比弧与“是”的关系,朱再玉提供了一种新的“是”弧的方法,其准确度高于郭守敬的方法。在此基础上,对胡适新方法的构造进行了检索,发现朱在禹创造了一种新的插值方法。根据朱在宇的说法,在每一步中使用线性插值来修改系数,然后通过重复这些步骤来构造一个高阶多项式函数。朱在禹的插补方法是机械式的,用这种方法构造的多项式函数被归类为牛顿插补的类型,特别是在现代术语中。中国古代历法编者插值的关键目的是构造高次多项式函数;重要的是,朱在禹对这一问题给出了一般性的解决方案。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A neglected text: the new method of Hu Shi and Zhu Zaiyu’s interpolation

This paper translates and interprets a neglected and significant original text in Zhu Zaiyu’s 朱載堉 (1536–1611) calendar system. The invention and application of Guo Shoujing’s 郭守敬 (1231–1316) hushi geyuan 弧矢割圓 was a great change in the concept of constructing calendar system. In this text we argue that, by giving the relationship between xian-hu 弦弧 ratio and shi 矢, Zhu Zaiyu provided a new method of hu shi 弧矢新術 with higher accuracy than Guo Shoujing’s. Furthermore, we retrieved the construction of the new method of hu shi and discovered the crucial fact that Zhu Zaiyu created a new interpolation method. According to Zhu Zaiyu, a linear interpolation was used to modify the coefficient in each single step, then by repeating the steps, a high-order polynomial function could be constructed. Zhu Zaiyu’s interpolation was mechanical, and the polynomial function constructed by this method was categorized as the type of Newton interpolation, notably in modern terms. The critical purpose of ancient Chinese calendar compilers in interpolation was to construct higher order polynomial function; crucially, Zhu Zaiyu gave a general solution to this problem.

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来源期刊
Archive for History of Exact Sciences
Archive for History of Exact Sciences 管理科学-科学史与科学哲学
CiteScore
1.30
自引率
20.00%
发文量
16
审稿时长
>12 weeks
期刊介绍: The Archive for History of Exact Sciences casts light upon the conceptual groundwork of the sciences by analyzing the historical course of rigorous quantitative thought and the precise theory of nature in the fields of mathematics, physics, technical chemistry, computer science, astronomy, and the biological sciences, embracing as well their connections to experiment. This journal nourishes historical research meeting the standards of the mathematical sciences. Its aim is to give rapid and full publication to writings of exceptional depth, scope, and permanence.
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