牛顿论几何学中的构造

IF 0.5 3区 哲学 Q3 HISTORY & PHILOSOPHY OF SCIENCE
Viktor Blåsjö
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引用次数: 0

摘要

牛顿对笛卡尔围绕某些曲线追踪原理组织几何基础的建构主义观点持批评态度。在未发表的著作中,牛顿以他的 "有机 "曲线追踪法为基础,概述了自己的建构主义方案,该方案将笛卡尔标志性的转尺移动曲线构建法作为特例归入其中,但没有后者无法追踪所有圆锥曲线的缺陷。人们对牛顿的这一方案研究甚少,但它比人们通常所认识到的更加深思熟虑,技术含量更高。它还与牛顿早先关于这一主题的著名论述相冲突,也可以说是对其的超越和改进。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Newton on constructions in geometry

Newton was critical of Descartes's constructivist vision of the foundations of geometry organised around certain curve-tracing principles. In unpublished work, Newton outlined a constructivist program of his own, based on his “organic” method of curve tracing, which subsumes Descartes's emblematic turning-ruler-and-moving-curve construction method as a special case, but does not suffer from the latter's flaw of being unable to trace all conics. This Newtonian program has been little studied and is more thoughtful and technically substantive than is commonly recognised. It also clashes with, and arguably supersedes and improves upon, Newton's perhaps better known earlier statements on the subject.

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来源期刊
Historia Mathematica
Historia Mathematica 数学-科学史与科学哲学
CiteScore
1.10
自引率
0.00%
发文量
29
审稿时长
72 days
期刊介绍: Historia Mathematica publishes historical scholarship on mathematics and its development in all cultures and time periods. In particular, the journal encourages informed studies on mathematicians and their work in historical context, on the histories of institutions and organizations supportive of the mathematical endeavor, on historiographical topics in the history of mathematics, and on the interrelations between mathematical ideas, science, and the broader culture.
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