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

IF 0.7 2区 哲学 Q2 HISTORY & PHILOSOPHY OF SCIENCE Archive for History of Exact Sciences Pub Date : 2020-01-10 DOI:10.1007/s00407-019-00244-w
Andrea Del Centina, Alessandra Fiocca
{"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,&nbsp;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":null,"pages":null},"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,&nbsp;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\":null,\"pages\":null},\"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}
引用次数: 2

摘要

为了解决当轨迹是椭圆并且力指向其中心时的中心力的直接问题,牛顿使用了著名的引理12(Principia,I,sect.II),该引理后来被认为相当于阿波罗圆锥曲线第七卷的命题31。在这篇论文中,我们为引理12寻找牛顿的可能来源,我们将Borelli编辑的Apolonius的原始证明与其他作者的证明进行了比较,包括牛顿自己给出的证明。此外,在追溯了其编辑历史后,我们评估了博雷利版《阿波罗的圆锥曲线》第V-VII卷在《原理》印刷之前的传播情况。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

摘要图片

查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
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.

求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
Archive for History of Exact Sciences
Archive for History of Exact Sciences 管理科学-科学史与科学哲学
CiteScore
1.30
自引率
20.00%
发文量
16
审稿时长
>12 weeks
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.
期刊最新文献
Felix Klein and Sophus Lie on quartic surfaces in line geometry Einstein–Perrin dilemma on the Brownian motion (Avogadro’s number) resolved? Some remarks on the history of Ricci’s absolute differential calculus Archimedean solids in the fifteenth and sixteenth centuries Quantum mechanics, radiation, and the equivalence proof
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1