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題 名 | 關於正負開方術發展歷史的討論=A Study on the History of the Positive-Negative Root Extraction Algorithm in Ancient China |
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作 者 | 王榮彬; | 書刊名 | 清華學報 |
卷 期 | 28:1 1998.03[民87.03] |
頁 次 | 頁1-18 |
分類號 | 311.11 |
關鍵詞 | 中國古算; 正負開方術; 劉益; 賈憲; Mathematics in ancient China; The positive negative root extraction algorithm; Liu yi; Jia xian; |
語 文 | 中文(Chinese) |
中文摘要 | 本文通過考察楊輝對劉益和賈憲有關開方術工作的徵引,認為在賈憲、劉益之 前(大約10世紀中晚期),中算家探索出了增乘法以及增乘開方法,進而使開方術發展到了 開任意高次冪,並且在不斷運用增乘開方法過程中發現了開方作法本源圖。11世紀,劉益 將開方術拓展到正負開方術。正負開方術的估根十分困難,而這一難題則成了清中葉方程 理論研究的主要動因。 |
英文摘要 | By examining the records of Jia Xian's (fl. 1023-1050) and Liu Yi's (c. 1080) methods for root extraction quoted by Yang Hui (fl. 1261-1275), the author of this paper has the following ideas for the developing course of the Positive-Negative Root Extraction Algorithm in ancient China. About in the later half of the 10th century, ancient Chinese mathematiclans invented the Zengcheng Method and the Zengcheng Root Extractioil Algorithm. The Zengcheng Root Extraction Algorithm is a kind of mechanized algorithm and could be easily extended to the general method for solving algebraic equations with positive coefficients of any degree. And in the course of continuously using this algorithm, the ancient Chinese mathematicians found Table of the Origin of the Method for Root Extraction. About in the 11th century, Liu Yi improved the method for root extraction to the Positive Negative Root Extraction Algorithm. The method of estimating roots in this algorithm is very difficult, and mainly owing to this difficult problem, the theory of algebraic equations was far developed in the mid-Qing Dynasty. |
本系統中英文摘要資訊取自各篇刊載內容。