等价形式的永恒性原理——皮考克的符号代数

Principle of the permanence of equivalent forms:George Peacock's symbolical algebra

目的系统探讨和研究皮考克(George Peacock,1791—1858)的符号代数思想。方法文献考证和历史分析。结果皮考克(George Peacock,1791—1858)的符号代数是在利用抽象符号的运算法则所决定的代数结构来确立负数和虚数的"合法化"基础时创造的一种新科学,是将算术代数中的规则通过"等价形式的永恒性原理"进行扩展得出的。结论皮考克的代数思想为纯粹形式代数的产生铺平了道路,尤其是直接影响了布尔逻辑代数思想的形成。

Aim To systematically discuss and research George Peacock＇s symbolical algebra. Methods Using the method of detailed literature investigation and historical analysis. Results Peacock＇s symbolical algebra is a new science when he used the algebraic structure decided by algorithm of abstract signs to solve the problem of the legitimate foundation of negative and imaginary numbers, induced by generalizing the rule of arithmetic algebra through ＂principle of the permanence of equivalent forms＂. Conclusion Peacock＇ symbolical algebra paves way for pure formal algebra and creates a prerequisite for the free of algebra.