中文摘要：

目的以新的角度阐释阿贝尔关于一般五次方程不可解的证明过程，为这一思想的来源及演进提供新的线索。方法以对原文及相关著作的研究为基础，对数学内在思想联系进行分析及推理。结果拉格朗日（1736-1813）、高斯（1777-1855）等人对代数方程可解的定义及革新是阿贝尔（1802--1829）证明的思想基础。结论从数学史发展的角度，便能清楚地看到新的数学内容的发现及数学结构的完整都并非凭空产生，而是沿着数学内在的严密逻辑和方法建立起来的。

英文摘要：

Aim Making the development history of procedure of the proof on the unsolvability of general equation theory as the mainline of the paper, to explore the quintic equation from a new perspective; to provide new way and information for understanding the emergence of Abel＇s thoughts. Methods Based on studying the original pa- pers and other related works, to analyze and deduce the mathematical thoughts contained in the proof. Results The definition and revision by Lagrange and Gauss for the solvability of algebraic equations laid foundations for the idea of Abel＇s proof. Conclusion It is clear that the discovery of new mathematical facts could not come into being without previous works, and they must be established along the inner strict logic and based on former methods in mathematics.