Pub Date : 2022-05-01DOI: 10.1016/j.hm.2020.12.002
Xiaofei Wang
At the turn of the 19th century, arithmetic underwent a reform. Lagrange and Delambre developed diverse reflections on this discipline and contributed to the revival of the study of the ancient Greeks' mathematics. Through analyzing Lagrange's lectures on arithmetic and the popular arithmetic treatises, I reestablish how Lagrange's innovative ideas were adopted in the later books. Moreover, this paper clarifies the role that “complex numbers” played in these treatises and investigates Delambre's memoir on the ancient Greek arithmetic, so as to reveal the way in which Delambre read the ancients' texts and reconstructed their arithmetic using “complex numbers”.
{"title":"How Jean-Baptiste Delambre read ancient Greek arithmetic on the basis of the arithmetic of “complex numbers” at the turn of the 19th century","authors":"Xiaofei Wang","doi":"10.1016/j.hm.2020.12.002","DOIUrl":"10.1016/j.hm.2020.12.002","url":null,"abstract":"<div><p>At the turn of the 19th century, arithmetic underwent a reform. Lagrange and Delambre developed diverse reflections on this discipline and contributed to the revival of the study of the ancient Greeks' mathematics. Through analyzing Lagrange's lectures on arithmetic and the popular arithmetic treatises, I reestablish how Lagrange's innovative ideas were adopted in the later books. Moreover, this paper clarifies the role that “complex numbers” played in these treatises and investigates Delambre's memoir on the ancient Greek arithmetic, so as to reveal the way in which Delambre read the ancients' texts and reconstructed their arithmetic using “complex numbers”.</p></div>","PeriodicalId":51061,"journal":{"name":"Historia Mathematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.hm.2020.12.002","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41490667","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-02-01DOI: 10.1016/j.hm.2022.01.003
Henry Zepeda, Benno van Dalen, Menso Folkerts
{"title":"In memoriam: Richard P. Lorch (1942–2021)","authors":"Henry Zepeda, Benno van Dalen, Menso Folkerts","doi":"10.1016/j.hm.2022.01.003","DOIUrl":"10.1016/j.hm.2022.01.003","url":null,"abstract":"","PeriodicalId":51061,"journal":{"name":"Historia Mathematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0315086022000039/pdfft?md5=f5490f0cc53093de78ebbe54d4d2599a&pid=1-s2.0-S0315086022000039-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42156895","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-02-01DOI: 10.1016/j.hm.2021.09.002
Christián C. Carman
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.
{"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":"10.1016/j.hm.2021.09.002","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":0.5,"publicationDate":"2022-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41537447","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-02-01DOI: 10.1016/j.hm.2021.07.004
Charlotte de Varent
This study is based on a set of six tablets dated to the Old-Babylonian period in Mesopotamia, written in cuneiform script, and relating to problems on the areas of squares. Their content is very similar, except for the length measurement of the side of the square. The issue of hypothetical pedagogical issues involved in the choice of numerical values in the statements is addressed by detailing the tasks they imply in the process of problem solving.
{"title":"Small numerical variations in a set of similar problems from Nippur on the area of the square","authors":"Charlotte de Varent","doi":"10.1016/j.hm.2021.07.004","DOIUrl":"10.1016/j.hm.2021.07.004","url":null,"abstract":"<div><p>This study is based on a set of six tablets dated to the Old-Babylonian period in Mesopotamia, written in cuneiform script, and relating to problems on the areas of squares. Their content is very similar, except for the length measurement of the side of the square. The issue of hypothetical pedagogical issues involved in the choice of numerical values in the statements is addressed by detailing the tasks they imply in the process of problem solving.</p></div>","PeriodicalId":51061,"journal":{"name":"Historia Mathematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41929531","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-02-01DOI: 10.1016/j.hm.2022.01.004
Reinhard Siegmund-Schultze
{"title":"From lattices via social history to theories of modernity in mathematics","authors":"Reinhard Siegmund-Schultze","doi":"10.1016/j.hm.2022.01.004","DOIUrl":"10.1016/j.hm.2022.01.004","url":null,"abstract":"","PeriodicalId":51061,"journal":{"name":"Historia Mathematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0315086022000040/pdfft?md5=815efdef4bcb218c5f5814a23a47255f&pid=1-s2.0-S0315086022000040-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49068239","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-02-01DOI: 10.1016/j.hm.2021.07.003
Lene Birkeland, Rolf Nossum
The biographical literature on Sofya Vasilyevna Kovalevskaya has to a large extent relied on her own memoirs, published in Vestnik Evropy only months before her death, and an autobiographical story published posthumously in Russkaya Starina. In this paper we present and discuss the full Russian text with English translation of a letter, previously unpublished, from Kovalevskaya's teacher in childhood and adolescence, Iosif Ignatyevich Malevich, to the editor of Russkaya Starina, Mikhail Ivanovich Semevsky, in which he repudiates her depreciation of his role in her schooling, criticizes her self-portrayal, and provides information about her early education which runs counter to parts of the biographical literature on Kovalevskaya.
{"title":"A letter from Malevich to Semevsky about Kovalevskaya","authors":"Lene Birkeland, Rolf Nossum","doi":"10.1016/j.hm.2021.07.003","DOIUrl":"10.1016/j.hm.2021.07.003","url":null,"abstract":"<div><p>The biographical literature on Sofya Vasilyevna Kovalevskaya has to a large extent relied on her own memoirs, published in <em>Vestnik Evropy</em> only months before her death, and an autobiographical story published posthumously in <em>Russkaya Starina</em>. In this paper we present and discuss the full Russian text with English translation of a letter, previously unpublished, from Kovalevskaya's teacher in childhood and adolescence, Iosif Ignatyevich Malevich, to the editor of <em>Russkaya Starina</em>, Mikhail Ivanovich Semevsky, in which he repudiates her depreciation of his role in her schooling, criticizes her self-portrayal, and provides information about her early education which runs counter to parts of the biographical literature on Kovalevskaya.</p></div>","PeriodicalId":51061,"journal":{"name":"Historia Mathematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0315086021000641/pdfft?md5=d94a5881216d47a6cc0edfe064dbb8db&pid=1-s2.0-S0315086021000641-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46763395","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-02-01DOI: 10.1016/S0315-0860(22)00015-5
{"title":"Notes on contributors","authors":"","doi":"10.1016/S0315-0860(22)00015-5","DOIUrl":"https://doi.org/10.1016/S0315-0860(22)00015-5","url":null,"abstract":"","PeriodicalId":51061,"journal":{"name":"Historia Mathematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"137332344","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-11-01DOI: 10.1016/S0315-0860(21)00081-1
{"title":"Notes on contributors","authors":"","doi":"10.1016/S0315-0860(21)00081-1","DOIUrl":"https://doi.org/10.1016/S0315-0860(21)00081-1","url":null,"abstract":"","PeriodicalId":51061,"journal":{"name":"Historia Mathematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136810249","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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