{"title":"The first six propositions of Archimedes' <i>on equilibrium of planes</i> 1.","authors":"Jean De Groot","doi":"10.1080/00033790.2024.2349878","DOIUrl":null,"url":null,"abstract":"<p><p>Modern commentators have doubts about the authenticity and cogency of the early propositions of Archimedes' <i>On Equilibrium of Planes</i> Book 1. Ernst Mach famously said that the proof of Prop. 6, the so-called law of the lever, assumes what is to be proven. Comparing the initial text in Heiberg's modern edition (1881, 1913) to the first propositions in Eutocius' commentary on <i>EP</i> 1, J. L. Berggren ([1976]. 'Spurious Theorems in Archimedes' Equilibrium of Planes: Book I', <i>Archive for History of Exact Sciences</i> 16.2 (1976), 87-103.) claimed that the propositions up through Proposition 3 of the standard modern edition are schoolbook additions written by an ancient author inferior to Archimedes. The present paper argues for the logical connectedness of Postulates 1-5 to Props. 1-6, by means of a detailed examination of the course of the argument and a re-examination of Eutocius' remarks. The paper reinterprets the role of the empirical in the early propositions and offers a reading of the contribution of Archimedes' mechanics to the method of <i>EP</i> 1.</p>","PeriodicalId":8086,"journal":{"name":"Annals of Science","volume":null,"pages":null},"PeriodicalIF":0.9000,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of Science","FirstCategoryId":"98","ListUrlMain":"https://doi.org/10.1080/00033790.2024.2349878","RegionNum":3,"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: 0
Abstract
Modern commentators have doubts about the authenticity and cogency of the early propositions of Archimedes' On Equilibrium of Planes Book 1. Ernst Mach famously said that the proof of Prop. 6, the so-called law of the lever, assumes what is to be proven. Comparing the initial text in Heiberg's modern edition (1881, 1913) to the first propositions in Eutocius' commentary on EP 1, J. L. Berggren ([1976]. 'Spurious Theorems in Archimedes' Equilibrium of Planes: Book I', Archive for History of Exact Sciences 16.2 (1976), 87-103.) claimed that the propositions up through Proposition 3 of the standard modern edition are schoolbook additions written by an ancient author inferior to Archimedes. The present paper argues for the logical connectedness of Postulates 1-5 to Props. 1-6, by means of a detailed examination of the course of the argument and a re-examination of Eutocius' remarks. The paper reinterprets the role of the empirical in the early propositions and offers a reading of the contribution of Archimedes' mechanics to the method of EP 1.
现代评论家对阿基米德《论平面平衡》第一卷早期命题的真实性和说服力表示怀疑。恩斯特-马赫说过一句名言：命题6的证明，即所谓的杠杆定律，假定了要证明的东西。J. L. Berggren（[1976].阿基米德《平面平衡》中的虚假定理：Book I'，Archive for History of Exact Sciences 16.2 (1976)，87-103.)声称，标准现代版中命题 3 之前的命题是由一位不如阿基米德的古代作者编写的教科书增补内容。本文论证了命题1-5与命题1-6之间的逻辑联系。本文通过对论证过程的详细考察和对欧托西乌斯言论的重新审视，论证了公设1-5与公设1-6之间的逻辑联系。本文重新解释了经验在早期命题中的作用，并解读了阿基米德力学对EP 1方法的贡献。
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Annals of Science , launched in 1936, publishes work on the history of science, technology and medicine, covering developments from classical antiquity to the late 20th century. The Journal has a global reach, both in terms of the work that it publishes, and also in terms of its readership. The editors particularly welcome submissions from authors in Asia, Africa and South America.
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