{"title":"Poncelet's discovery of homology","authors":"Christopher Baltus","doi":"10.1016/j.hm.2022.12.001","DOIUrl":null,"url":null,"abstract":"<div><p><span><em>Homology</em></span> was among the concepts introduced in Jean Victor Poncelet's 1822 <em>Traité des Propriétés Projectives des Figures</em>. Homology is a projective transformation which has an axis, a line of fixed points. The <em>Traité</em> develops a straightedge construction of points under <em>homology</em>, essentially that found in work on perspective drawing and by Phillipe de la Hire, 1673. However, Poncelet's very distinct path to homology was through <em>similitude</em><span>, where the radical axis of a pair of circles became the axis of homology. We end with Poncelet's application of homology involving the focus of a conic section.</span></p></div>","PeriodicalId":51061,"journal":{"name":"Historia Mathematica","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Historia Mathematica","FirstCategoryId":"98","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0315086022000878","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: 0
Abstract
Homology was among the concepts introduced in Jean Victor Poncelet's 1822 Traité des Propriétés Projectives des Figures. Homology is a projective transformation which has an axis, a line of fixed points. The Traité develops a straightedge construction of points under homology, essentially that found in work on perspective drawing and by Phillipe de la Hire, 1673. However, Poncelet's very distinct path to homology was through similitude, where the radical axis of a pair of circles became the axis of homology. We end with Poncelet's application of homology involving the focus of a conic section.
同调是让-维克托·庞塞莱1822年的《人物投影》中引入的概念之一。同调是一个投影变换，它有一个轴，一条不动点线。Traité在同源性下发展了一种点的直边构造，本质上是在透视图和Phillipe de la Hire的作品中发现的，1673年。然而，庞塞莱通往同源性的独特途径是通过相似，其中一对圆的根轴成为同源轴。我们以庞塞莱的同调应用结束，同调涉及圆锥截面的焦点。
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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