{"title":"François Viète's method for calculating the eccentricity in a bisected model and its possible application to Kepler's Vicarious Hypothesis","authors":"Christián C. Carman","doi":"10.1016/j.hm.2021.09.002","DOIUrl":null,"url":null,"abstract":"<div><p>According to Kepler's own words in <em>Astronomia Nova</em>, he invested five years trying to find the values for the eccentricities for his “vicarious” hypothesis. At some point, he asked Herwart von Hohenburg, to ask François Viète's help to solve his problem, but there is no evidence that Viète received this request. At that time, Viète was working on his unpublished <em>Ad harmonicon coeleste</em>. In it, he proposes a new method for bisected models, which can easily be extended to non-bisected models. In this paper, I describe Viète's method, analyze its accuracy, and show how to extend it to non-bisected models, making it suitable for solving Kepler's problem.</p></div>","PeriodicalId":51061,"journal":{"name":"Historia Mathematica","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2022-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Historia Mathematica","FirstCategoryId":"98","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0315086021000665","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: 1
Abstract
According to Kepler's own words in Astronomia Nova, he invested five years trying to find the values for the eccentricities for his “vicarious” hypothesis. At some point, he asked Herwart von Hohenburg, to ask François Viète's help to solve his problem, but there is no evidence that Viète received this request. At that time, Viète was working on his unpublished Ad harmonicon coeleste. In it, he proposes a new method for bisected models, which can easily be extended to non-bisected models. In this paper, I describe Viète's method, analyze its accuracy, and show how to extend it to non-bisected models, making it suitable for solving Kepler's problem.
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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