{"title":"论19世纪初马斯切罗尼的《圆规几何》","authors":"Michael Friedman","doi":"10.1016/j.hm.2021.05.002","DOIUrl":null,"url":null,"abstract":"<div><p>Lorenzo <span>Mascheroni</span>'s <span>1797</span> work <em>La geometria del compasso</em><span><span>, which develops a geometry based solely on compass constructions, is considered by the author as stepping back behind the “demarcation line” of Euclidean geometry. In this work Mascheroni emphasizes the practical aspects of this geometry over a theoretical approach. A century later, in 1899, </span>David Hilbert and his student Michael Feldblum proposed a totally different approach – algebraic and axiomatic – concerning geometric constructions based on various instruments. Taking into account that, at the end of the 18th century, straightedge geometry was also developed, one may ask what happened to the image of instrument-based geometry during the 19th century? By focusing on Mascheroni's book and its reception, this article aims to examine the various views and conceptions of mathematicians with respect to this geometry.</span></p></div>","PeriodicalId":51061,"journal":{"name":"Historia Mathematica","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.hm.2021.05.002","citationCount":"1","resultStr":"{\"title\":\"On Mascheroni's La geometria del compasso at the beginning of the 19th century\",\"authors\":\"Michael Friedman\",\"doi\":\"10.1016/j.hm.2021.05.002\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Lorenzo <span>Mascheroni</span>'s <span>1797</span> work <em>La geometria del compasso</em><span><span>, which develops a geometry based solely on compass constructions, is considered by the author as stepping back behind the “demarcation line” of Euclidean geometry. In this work Mascheroni emphasizes the practical aspects of this geometry over a theoretical approach. A century later, in 1899, </span>David Hilbert and his student Michael Feldblum proposed a totally different approach – algebraic and axiomatic – concerning geometric constructions based on various instruments. Taking into account that, at the end of the 18th century, straightedge geometry was also developed, one may ask what happened to the image of instrument-based geometry during the 19th century? By focusing on Mascheroni's book and its reception, this article aims to examine the various views and conceptions of mathematicians with respect to this geometry.</span></p></div>\",\"PeriodicalId\":51061,\"journal\":{\"name\":\"Historia Mathematica\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2021-11-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/j.hm.2021.05.002\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Historia Mathematica\",\"FirstCategoryId\":\"98\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0315086021000409\",\"RegionNum\":3,\"RegionCategory\":\"哲学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"HISTORY & PHILOSOPHY OF SCIENCE\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Historia Mathematica","FirstCategoryId":"98","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0315086021000409","RegionNum":3,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"HISTORY & PHILOSOPHY OF SCIENCE","Score":null,"Total":0}
引用次数: 1
摘要
洛伦佐·马斯切罗尼(Lorenzo Mascheroni)在1797年的著作《圆规几何》(La geomeia del compasso)发展了一种完全基于圆规结构的几何,作者认为这是倒退到欧几里得几何的“分界线”后面。在这部作品中,Mascheroni强调了这种几何的实践方面,而不是理论方法。一个世纪后,在1899年,大卫·希尔伯特和他的学生迈克尔·费尔德布伦提出了一种完全不同的方法——代数和公理化——关于基于各种仪器的几何构造。考虑到在18世纪末,直线几何也得到了发展,人们可能会问,19世纪基于仪器的几何图像发生了什么变化?通过关注马斯切罗尼的书及其接受情况,本文旨在研究数学家关于这种几何的各种观点和概念。
On Mascheroni's La geometria del compasso at the beginning of the 19th century
Lorenzo Mascheroni's 1797 work La geometria del compasso, which develops a geometry based solely on compass constructions, is considered by the author as stepping back behind the “demarcation line” of Euclidean geometry. In this work Mascheroni emphasizes the practical aspects of this geometry over a theoretical approach. A century later, in 1899, David Hilbert and his student Michael Feldblum proposed a totally different approach – algebraic and axiomatic – concerning geometric constructions based on various instruments. Taking into account that, at the end of the 18th century, straightedge geometry was also developed, one may ask what happened to the image of instrument-based geometry during the 19th century? By focusing on Mascheroni's book and its reception, this article aims to examine the various views and conceptions of mathematicians with respect to this geometry.
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.