{"title":"Desargues’s concepts of involution and transversal, their origin, and possible sources of inspiration","authors":"Andrea Del Centina","doi":"10.1007/s00407-022-00296-5","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we try to understand what considerations and possible sources of inspiration Desargues used to formulate his concepts of involution and transversal, and to state the related theorems that are at the basis of his <i>Brouillon project</i>. To this end, we trace some clues which are found scattered throughout his works, we connect them together in the light of his experience and knowledge in the field of perspective, and we investigate what were his motivations within Mersenne’s academy. As a result of our research, we can safely say that were his great geometrical insight and his projective vision of space which, guided by some classical theorems, led him to these completely new concepts in the <i>panorama</i> of the geometry of that time that were destined to remain misunderstood for about two centuries.</p></div>","PeriodicalId":50982,"journal":{"name":"Archive for History of Exact Sciences","volume":"76 6","pages":"573 - 622"},"PeriodicalIF":0.7000,"publicationDate":"2022-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00407-022-00296-5.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Archive for History of Exact Sciences","FirstCategoryId":"98","ListUrlMain":"https://link.springer.com/article/10.1007/s00407-022-00296-5","RegionNum":2,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"HISTORY & PHILOSOPHY OF SCIENCE","Score":null,"Total":0}
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Abstract
In this paper, we try to understand what considerations and possible sources of inspiration Desargues used to formulate his concepts of involution and transversal, and to state the related theorems that are at the basis of his Brouillon project. To this end, we trace some clues which are found scattered throughout his works, we connect them together in the light of his experience and knowledge in the field of perspective, and we investigate what were his motivations within Mersenne’s academy. As a result of our research, we can safely say that were his great geometrical insight and his projective vision of space which, guided by some classical theorems, led him to these completely new concepts in the panorama of the geometry of that time that were destined to remain misunderstood for about two centuries.
期刊介绍：
The Archive for History of Exact Sciences casts light upon the conceptual groundwork of the sciences by analyzing the historical course of rigorous quantitative thought and the precise theory of nature in the fields of mathematics, physics, technical chemistry, computer science, astronomy, and the biological sciences, embracing as well their connections to experiment. This journal nourishes historical research meeting the standards of the mathematical sciences. Its aim is to give rapid and full publication to writings of exceptional depth, scope, and permanence.
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