Mathematical and Historical Study of Shou Shi Li and its Acceptance in Japan in the Seventeenth Century

受十理的数理和历史研究及其在 17 世纪日本的接受

基本信息

批准号：
11680008
负责人：
OGAWA Tsukane
金额：
$ 0.51万
依托单位：
Yokkaichi University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1999
资助国家：
日本
起止时间：
1999 至 2000
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-11680008/
关键词：
Shou Shi Li Winter and Summer Solstice Zu Chongzhi 冬至計算夏至計算

项目摘要

1.We classified patterns of calculation of the winter or summer solstice in Shou Shi Li, the last method of establishing the calendar before the Ming dynasty in China, and made a strict interpretation of the original text on the basis of this classification. Some parts of the text have ambiguous expressions and we cannot interpret them when we only consider each phrase in question. Our approach is valid for this question. We can determine the interpretations of paragraphs 3-6 about the winter solstice in 1277, paragraphs 3-10 about summer solstice and paragraph 3 about winter solstice in 1278, and paragraphs 3, 5-7, 11, and 13 about winter solstice in 1279.2.Zu Chongzhi(429-500)computed the time of a tropical year from three data of measuring shadow length. This method, the Zu Chongzhi's method, was very popular in Chinese astronomy, Wang Xun, Guo Shoujing used this method and computed the time span of one tropical year, 365.2425 days. Zu supposed that the function of shadow length was symmetry and computed the ratio of changing shadow length. Historians of astronomy in modern Japanese called the Zu's method to the "incline method" because Zu supposed that the ratio of changing shadow length was the liner. However there were some historical materials in China that this method was named the Zu's method. And Huang Ding also described this method, Zu Chongzhi method, in the "Tianwen Dacheng Guankui Jiyao"(1653). Then Seki Takakazu(Kowa)(1642? -1708)studied and arranged this book. Therefore Japanese mathematician in the Edo period knew this method and its name.

1.我们对中国明代以前最后一种历法《守时历》中冬至或夏至的计算方式进行了分类，并在此分类的基础上对原文进行了严格的解释。文本的某些部分有歧义，当我们只考虑每个短语时，我们无法解释它们。我们的方法对于这个问题是有效的。我们可以确定1277年关于冬至的第3-6段，1278年关于夏至的第3-10段和关于冬至的第3段，以及1279.2关于冬至的第3、5-7、11和13段的解释。 .祖冲之(429-500)根据三个数据计算回归年的时间测量阴影长度。这种方法，即祖冲之法，在中国天文学中非常流行，王训、郭守敬等都用这种方法计算出了回归年的时间跨度，即365.2425天。祖认为阴影长度的函数是对称的，并计算了阴影长度变化的比率。日本现代天文学家将祖氏的方法称为“倾斜法”，因为祖氏认为影子长度变化的比率就是直线。但中国有一些史料称这种方法被称为祖氏法。而黄鼎在《天问大成观葵基要》(1653)中也描述了这种方法，即祖冲之法。随后关高和（Kowa）（1642？-1708）研究并整理了这本书。因此，江户时代的日本数学家就知道这种方法及其名称。