关于牛顿著作《广义算术》形成及其内容与影响的研究

Research on Formation of Newton’s Work Universal Arithmetic and Its Content and Influence

牛顿于1707年出版的代数学著作《广义算术》在随后的三个多世纪里,影响了一大批欧洲的数学家和科学家学习数学。近年来,随着对牛顿数学和科学研究的不断开展,越多越多的人对牛顿的这本代数学著作进行讨论。本文运用文献分析法,结合牛顿的原著和当时的数学工作,对以往此类相关研究进行归纳和梳理,发现已有的研究主要集中在出版、内容来源、具体内容分析、其中的数学思想方法及其影响这五个方面;但这五个方面多数都研究得不是很全面,也不深入;现在研究比较深入的仅是其中牛顿给出的圆锥曲线构造理论和确定方程虚根和范围的方法两个具体方面,这是当前研究的热点之一。建议后续的研究更多关注此著作中内容的来源和其中反映出来的牛顿的数学思想方法。

Newton’s algebraic work Universal Arithmetic published in 1707 influenced a large number of Eu-ropean mathematicians and scientists to learn mathematics in the following three centuries. Re-cently, with the continuous development of research on Newton’s mathematics and science, more and more scholars have discussed this book. This paper combined Newton’s original works and the mathematical work at that time and sorted out the previous relevant research by means of litera-ture analysis, and found that the existing research mainly focuses on five aspects, that is the publication, content sources, specific content analysis, mathematical thoughts and methods and their influence. However, most of these five aspects are not comprehensive or in-depth except for two specific aspects which are the conic construction theory, which is one of the current research hotspots, given by Newton and the method of determining the imaginary root and range of the equation. It is suggested that the follow-up research should pay more attention to the source of the content in this book and Newton’s mathematical thinking method reflected in it.