{"title":"波雷利版本的阿波罗尼乌斯的《圆锥定理》的第v - 7卷,以及牛顿的《原理》的引理12","authors":"Andrea Del Centina, Alessandra Fiocca","doi":"10.1007/s00407-019-00244-w","DOIUrl":null,"url":null,"abstract":"<div><p>To solve the direct problem of central forces when the trajectory is an ellipse and the force is directed to its centre, Newton made use of the famous Lemma 12 (<i>Principia</i>, I, sect. II) that was later recognized equivalent to proposition 31 of book VII of Apollonius’s <i>Conics</i>. In this paper, in which we look for Newton’s possible sources for Lemma 12, we compare Apollonius’s original proof, as edited by Borelli, with those of other authors, including that given by Newton himself. Moreover, after having retraced its editorial history, we evaluate the dissemination of Borelli's edition of books V-VII of Apollonius’s <i>Conics</i> before the printing of the <i>Principia</i>.</p></div>","PeriodicalId":50982,"journal":{"name":"Archive for History of Exact Sciences","volume":"74 3","pages":"255 - 279"},"PeriodicalIF":0.7000,"publicationDate":"2020-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s00407-019-00244-w","citationCount":"2","resultStr":"{\"title\":\"Borelli’s edition of books V–VII of Apollonius’s Conics, and Lemma 12 in Newton’s Principia\",\"authors\":\"Andrea Del Centina, Alessandra Fiocca\",\"doi\":\"10.1007/s00407-019-00244-w\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>To solve the direct problem of central forces when the trajectory is an ellipse and the force is directed to its centre, Newton made use of the famous Lemma 12 (<i>Principia</i>, I, sect. II) that was later recognized equivalent to proposition 31 of book VII of Apollonius’s <i>Conics</i>. In this paper, in which we look for Newton’s possible sources for Lemma 12, we compare Apollonius’s original proof, as edited by Borelli, with those of other authors, including that given by Newton himself. Moreover, after having retraced its editorial history, we evaluate the dissemination of Borelli's edition of books V-VII of Apollonius’s <i>Conics</i> before the printing of the <i>Principia</i>.</p></div>\",\"PeriodicalId\":50982,\"journal\":{\"name\":\"Archive for History of Exact Sciences\",\"volume\":\"74 3\",\"pages\":\"255 - 279\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2020-01-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1007/s00407-019-00244-w\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Archive for History of Exact Sciences\",\"FirstCategoryId\":\"98\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s00407-019-00244-w\",\"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}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Archive for History of Exact Sciences","FirstCategoryId":"98","ListUrlMain":"https://link.springer.com/article/10.1007/s00407-019-00244-w","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}
Borelli’s edition of books V–VII of Apollonius’s Conics, and Lemma 12 in Newton’s Principia
To solve the direct problem of central forces when the trajectory is an ellipse and the force is directed to its centre, Newton made use of the famous Lemma 12 (Principia, I, sect. II) that was later recognized equivalent to proposition 31 of book VII of Apollonius’s Conics. In this paper, in which we look for Newton’s possible sources for Lemma 12, we compare Apollonius’s original proof, as edited by Borelli, with those of other authors, including that given by Newton himself. Moreover, after having retraced its editorial history, we evaluate the dissemination of Borelli's edition of books V-VII of Apollonius’s Conics before the printing of the Principia.
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.