中國古代算學史研究新途徑－－以劉徽割圓術本土化研究為例

A New Approach to the Study of the History of Chinese Mathematics-The Case of the Localization Interpretation of Liu Hui's Geyuan Procedure

鞠實兒(Shier JU) ； 張一傑(Yijie ZHANG)

《哲學與文化》 44卷6期 (2017/06) Pp. 25-51

摘要

本文提出中國古代算學史的本土化研究程式，探索中國古代算學史的新途徑，並據此研究劉徽的割圓術。首先，從本土語境解讀《九章筭術》的「圓田術注」文本。然後，探討劉徽作注時所依賴的本土背景知識，闡明其造術時所採用的概念和方法。最後，在此基礎上，分析割圓術的論證結構，並進行本土解釋。本文指出：劉徽在割圓術中處理的圓和方是經驗物體，而非理念對象；借助基於經驗的有窮可分方法導出圓面積計算公式，而非基於極限理論的無窮小分析；割圓術文本是按「析理以辭，解體用圖」方式構造的廣義論證，而非從公理出發的演繹推理。

關鍵字

劉徽 ； 割圓術 ； 中國算學史 ； 本土解釋 ； 廣義論證

並列摘要

This article advances a procedure to study the localization explanation of the history of Chinese mathematics, and discuss a new approach to the study of the history of Chinese mathematics. Based on this, Liu Hui's Geyuan procedure is studied. Firstly, we read the text of the Yuantian procedure in its local context. Secondly, we analyze the local background knowledge Liu Hui replies on when he comments on the Nine Chapters on Mathematical Procedures, and illuminate the local concepts and methods he used to create this procedure. Finally, on this basis, we localizedly interpret the Geyuan procedure. This article indicates that the circles and the squares Liu Hui deals with in the Geyuan procedure are empirical matters rather than ideal objects. Relying on the empirical finite method to cut a circle, Liu Hui proves the area formula of a circle, and writes the text in which the general argumentation theory works, instead of using deductive inference, which is based on the infinitesimal analysis.

並列關鍵字

Liuhui ； Geyuan Procedure ； History of Chinese Mathematics ； Localization Interpretaion ； General Argumentation

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