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題名 | 從面積問題看《算學寶鑑》在中國傳統數學中的地位=An Analysis of Area Problems in the Suanxue Baojian |
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作者 | 郭書春; Guo, Shuchun; |
期刊 | 漢學研究 |
出版日期 | 20001200 |
卷期 | 18:2=37 2000.12[民89.12] |
頁次 | 頁197-221 |
分類號 | 310.92 |
語文 | chi |
關鍵詞 | 王文素; 算學寶鑑; 九章算法比類大全; 楊輝算法; 面積; Wang Wensu; Suanxue baojian; Jiuzhang suanfa bilei daquan; Yang Hui suanfa; Area problem; |
中文摘要 | 明朝王文素著的《算學寶鑑》(1524)是清朝《數理精蘊》問世(1723)前中國最大的一部數學著作。由於它成書四百餘年來未能刊刻,數學史界對之研究甚少,一般將其與吳敬的《九章算法比類大全》(1450)相提並論。本文認為,《算學寶鑑》的題目大都是從前輩數學著作中收集來的,只有「通證」、「新證」等部分才反映了王文素自己的思想。王文素未看到過《九章算術》,他所引用的所謂《九章》的內容,都源於吳敬的《九章算法比類大全》。本文著重分析了《算學寶鑑》中諸田求積、圓田求積、弧田論積三節的面積問題,指出王文素糾正了《五曹算經》、《九章算法比類大全》等著作中的若干錯誤公式,力求給出正確的求積公式。這說明《算學寶鑑》繼承了《九章算術》、《楊輝算法》等算法精確的傳統,與《九章算法比類大全》等有大量法理不通的算法是有根本區別的。因此,就中國傳統數學著作的分類上,《九章算法比類大全》是《五曹算經》等傳統的繼承者,而《算學寶鑑》則是《九章算術》、《楊輝算法》等傳統的繼承者。 |
英文摘要 | Prior to the completion of the Shuli jingyun 數理精蘊 (Sum of Essential Mathematical Principles) in 1723, the Suanxue baojian 算學寶鑑(Precious Mirror of Mathematics), written by Wang Wensu in the Ming Dynasty, was the largest Chinese mathematical work. Because it had never been published during the 400 years since it was written, there were few studies done on it. Generally, it was placed in the same category as the Jiuzhang suanfa bilei daquan 九章算法比類大全 (Classified Sum of Mathematical Methods in Nine Chapters of Mathematical Procedures). Relying on analysis of area problems in the Suanxue baojian, the author of this paper points out that Wang Wensu corrected some inaccurate formulas formulas contained in the Jiuzhang suanfa bilei daquan. Overall, the Suanxue baojian is characterized by accurate calculating methods and rigorous inference procedures. Therefore, in the classification of traditional mathematical works, the Suanxue baojian can be considered a descendent of the rigorous traditions of such works as Yang Hui suanfa 楊輝算法 (Yang Hui's Mathematical Methods), while the Jiuzhang suanfa bilei daquan is more in line with less exacting works like the Wucao suanjin 五曹算經 (Mathematical Manual of the Five Government Departments). |
本系統之摘要資訊系依該期刊論文摘要之資訊為主。