【摘要】：早期代數學最直接的目的是求解代數方程。本文以韋達(Francois Vieta,1540-1603)的著作合集《分析術》(TheAnalytic Art)中第四部分《方程的理解與修正》(Two Treatises on the Understanding and Amendment of Equations,1615)為主要研究內容,探究其對代數方程理論所做的貢獻。在前篇《方程的理解》(Firstreatise:On Understanding Equations)中,韋達分別運用符號分析法、二項式展開法和方程比較法分析了方程的結構;在后篇《方程的修正》(Seconnd Treatse:On the Amendment of Equations)中,韋達針對各類無法進行數值求解或者數值求解十分困難的方程提出了相應的方程變換法則,使其可以變換為能夠或者容易進行數值求解的新方程。韋達在前后兩篇中都是通過具體的定理或命題展示自己的研究結果,但僅對其中一部分給出了解釋或說明。本文目的在于遵循“古證復原”的原則分析這兩篇中的定理或命題,主要工作如下:第一,在探究韋達列方程的基本原則時,發(fā)現他強調方程與比例之間的聯系,所以本文研讀前篇《方程的理解》時,利用比例的思想復原了韋達在符號分析法與方程比較法中沒有解釋或說明的定理與命題,給出其較為合理的來源分析與證明,從而明確地得出,韋達思想的實質可歸結為恒等式變形。第二,分析后篇《方程的修正》中韋達提供的各類方程變換背后所蘊含的數學思想和方法,結合前篇中的符號分析法、二項式展開法和方程比較法對五種常用的方程變換進行探源,復原了韋達關于方程變換的部分定理,并指出其中的一條錯誤命題。
[Abstract]:The most direct purpose of early algebra is to solve algebraic equations. In this paper, the main content of this paper is "understanding and revising the equation" in the fourth part of "Analytical technique" (TheAnalytic Art) by Francois Vieta,1540-1603 (Two Treatises on the Understanding and Amendment of Equations,1615). To explore its contribution to the theory of algebraic equations. In the previous "understanding of equations" (Firstreatise:On Understanding Equations), Veda uses symbolic analysis method, binomial expansion method and equation comparison method to analyze the structure of the equation. In the latter part of "Correction of equations" (Seconnd Treatse:On the Amendment of Equations), Veda proposes the corresponding equation transformation rules for all kinds of equations which can not be solved numerically or which are very difficult to solve numerically. It can be transformed into a new equation that can be solved numerically or easily. In both the preceding and the following chapters, Veda presents his research results through specific theorems or propositions, but only gives explanations or explanations for some of them. The purpose of this paper is to analyze the theorems or propositions in these two chapters in accordance with the principle of "restoration of ancient evidence". The main work is as follows: first, when exploring the basic principles of the Vedalier equation, it is found that he emphasizes the relation between the equation and the proportion. So in this paper, when we read the previous book "understanding of equation", we use the idea of proportion to restore the theorems and propositions that Veda did not explain or explain in symbolic analysis and equation comparison, and give its more reasonable source analysis and proof. It is clear that the essence of Veda's thought can be summed up as identity deformation. Secondly, it analyzes the mathematical ideas and methods behind the transformation of all kinds of equations provided by Veda in the latter part of "Correction of the equation", and combines the symbolic analysis method in the previous chapter. In this paper, the binomial expansion method and the equation comparison method are used to explore the source of five kinds of commonly used equation transformations, and the partial theorems of Vedar's equation transformation are restored, and one of the wrong propositions is pointed out.
【學位授予單位】：西北大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：O151.1

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