中文摘要：

目的研究代数方程求解的历史，寻找代数方程求解内涵变更的关键点。方法采用原始文献考证和代数方程求解历史纵向比较的方法。结果Lagrange（1736-1813）用置换的思想进行代数方程求解是代数方程求解史中第一个转折点，它开辟了代数方程求解的新纪元，促进了代数方程求解的最终胜利，并引导了近代代数学的开始。结论Lagrange用置换的思想进行代数方程求解使数学家们从单纯的寻求代数技巧进行求解转变为寻找一种一般的、通用的解方程方法，并从繁重的数学计算中解脱出来，这种方法彻底改变了代数方程求解的内涵：从寻找求根公式到寻找预解式，并进行一系列的程序。

英文摘要：

Aim To study the history of solving algebraic equations and to find main points of the changing content of solving algebraic equations. Methods Methods of original article researching and comparing the history of sol- ving algebraic equations vertically. Results Lagrange applies the permutation theory to solve algebraic equations, which is the 1st turning point in the history of solving algebraic equations and also opens up a new era. Lagrange＇s Permutation Theory promoted the ultimate success of solving algebraic equations and guided the beginning of modem algebra. Conclusion This made the algebraists begin seeking a general, universal method to solve the algebraic equations instead of simply finding out an algebraic technique, which also made them free from toilsome calculating. This new method totally changes the content of solving algebraic equations： from searching for the root formula to finding a resolvent, and following the procedure.