微积分辩证认识简要

Brief Introduction to Understanding Dialectically the Infinitesimal Calculus

微积分在全部数学的历史中是一个最大创造,微积分发现的全部历史中,展现了辩证思维法的胜利,阿基米德的“穷竭法”,刘徽的“割圆术”,卡瓦列里的不可分量,费马的求切线方法,均是有力的说明。牛顿和莱布尼茨关于建立微积分而作出的杰出贡献,就在于他们分别提出了微积分的基本原理、三个重要概念:流量、流数、瞬和“变量”数学的思想体系。马克思和恩格斯则自觉地运用辩证方法对微积分作了深入探讨。

This article affirms first of all that the infinitesimal calculus -the biggest creature of the all mathematics - has its outstanding historical position, expounds the victory of dialectics in developing the history of discovering infinitesimal calculus. It has introduced the 'exhaustive method' of Archimedes, the 'cyclotomic skill' of liu hui, inseprable quantity of Cavalieri, the method of seeking tangent line of Fermart. This essay puts the stress on the introduction of outstanding contributions of Newton and Leibniz in their creatting infinitesimal calculus. They had put forward the basic principles of infinitesimal calculus, three important concepts: fluent, fluxion, moment and the systematic thoughts of 'variable' mathematics respectively. This article eulogizes also the revolutionary tutor Marx and Engels for their deeply approached infinitesimal calculus dialectically.