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Poincaré’s stated motivations for topology Poincaré关于拓扑的既定动机
IF 0.5 2区 哲学
Archive for History of Exact Sciences Pub Date : 2020-03-04 DOI: 10.1007/s00407-020-00247-y
Lizhen Ji, Chang Wang
{"title":"Poincaré’s stated motivations for topology","authors":"Lizhen Ji,&nbsp;Chang Wang","doi":"10.1007/s00407-020-00247-y","DOIUrl":"10.1007/s00407-020-00247-y","url":null,"abstract":"<div><p>It is well known that one of Poincaré’s most important contributions to mathematics is the creation of algebraic topology. In this paper, we examine carefully the stated motivations of Poincaré and potential applications he had in mind for developing topology. Besides being an interesting historical problem, this study will also shed some light on the broad interest of Poincaré in mathematics in a concrete way.</p></div>","PeriodicalId":50982,"journal":{"name":"Archive for History of Exact Sciences","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2020-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s00407-020-00247-y","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50449793","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Borelli’s edition of books V–VII of Apollonius’s Conics, and Lemma 12 in Newton’s Principia 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 0.5 2区 哲学
Archive for History of Exact Sciences Pub Date : 2020-01-10 DOI: 10.1007/s00407-019-00244-w
Andrea Del Centina, Alessandra Fiocca
{"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":"10.1007/s00407-019-00244-w","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":0.5,"publicationDate":"2020-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s00407-019-00244-w","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42702367","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
On Qin Jiushao’s writing system 论秦九韶的写作体系
IF 0.5 2区 哲学
Archive for History of Exact Sciences Pub Date : 2020-01-04 DOI: 10.1007/s00407-019-00243-x
Zhu Yiwen
{"title":"On Qin Jiushao’s writing system","authors":"Zhu Yiwen","doi":"10.1007/s00407-019-00243-x","DOIUrl":"10.1007/s00407-019-00243-x","url":null,"abstract":"<div><p>The <i>Mathematical Book in Nine Chapters</i>, written by Qin Jiushao in 1247, is a masterpiece that is representative of Chinese mathematics at that time. Most of the previous studies have focused on its mathematical achievements, while few works have addressed the counting diagrams that Qin used as a writing system. Based on a seventeenth-century copy of Qin’s treatise (i.e., Zhao Qimei’s 1616 handwritten copy), this paper systematically analyzes the writing system, which includes both a numeral system and a linear system. It argues that Qin provided a new representation of mathematics in addition to textual procedures, detailed solutions, and operations carried out with counting rods. Moreover, this new representation was used to connect mathematical practices within and outside the text and should be understood in its textual context. Therefore, Qin’s writing system represents an intermediate phase in the textualization and symbolization of Chinese mathematics in thirteenth-century China.\u0000</p></div>","PeriodicalId":50982,"journal":{"name":"Archive for History of Exact Sciences","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2020-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s00407-019-00243-x","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50448663","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
A proto-Normal Star Almanac dating to the reign of Artaxerxes III: BM 65156 阿尔塔薛西斯三世统治时期的原始恒星年鉴：BM 65156
IF 0.5 2区 哲学
Archive for History of Exact Sciences Pub Date : 2020-01-02 DOI: 10.1007/s00407-019-00246-8
John Steele
{"title":"A proto-Normal Star Almanac dating to the reign of Artaxerxes III: BM 65156","authors":"John Steele","doi":"10.1007/s00407-019-00246-8","DOIUrl":"10.1007/s00407-019-00246-8","url":null,"abstract":"<div><p>Babylonian methods for predicting planetary phenomena using the so-called goal-year periods are well known. Texts known as Goal-Year Texts contain collections of the observational data needed to make predictions for a given year. The predictions were then recorded in Normal Star Almanacs and Almanacs. Large numbers of Goal-Year Texts, Normal Star Almanacs and Almanacs are attested from the early third century BC onward. A small number of texts dating from before the third century present procedures for using the goal-year periods to predict planetary phenomena. In addition, two texts, one dating to the late sixth century BC and the other to the late fifth century BC, contain planetary data which was probably predicted using these methods. In this article, I discuss a further example of a tablet dating from before the third century BC which contains planetary data predicted using the goal-year periods. I show that the planetary phenomena contained in this tablet can be dated to the twelfth year of the reign of Artaxerxes III (347/6 BC) and that they were predicted using goal-year periods without the application of the kind of corrections which were used in the third century BC texts in order to produce more accurate predictions.</p></div>","PeriodicalId":50982,"journal":{"name":"Archive for History of Exact Sciences","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2020-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s00407-019-00246-8","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50439326","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Cracking bones and numbers: solving the enigma of numerical sequences on ancient Chinese artifacts 破解骨骼与数字：破解中国古代文物数字序列之谜
IF 0.5 2区 哲学
Archive for History of Exact Sciences Pub Date : 2019-12-10 DOI: 10.1007/s00407-019-00245-9
Andrea Bréard, Constance A. Cook
{"title":"Cracking bones and numbers: solving the enigma of numerical sequences on ancient Chinese artifacts","authors":"Andrea Bréard,&nbsp;Constance A. Cook","doi":"10.1007/s00407-019-00245-9","DOIUrl":"10.1007/s00407-019-00245-9","url":null,"abstract":"<div><p>Numerous recent discoveries in China of ancient tombs have greatly increased our knowledge of ritual and religious practices. These discoveries include excavated oracle bones, bronze, jade, stone and pottery objects, and bamboo manuscripts dating from the twelfth to fourth century BCE. Inscribed upon these artifacts are a large number of records of numerical sequences, for which no explanation has been found of how they were produced. Structural links to the <i>Book of Changes</i>, a divination manual that entered the Confucian canon, are evident; yet, the algorithm described therein dates to the slightly later second to first century BCE. By combining archeological and statistical evidence, we propose a new methodology that enables us to reconstruct and test cleromantic techniques which can explain how these numerical sequences were generated. Dice and divination stalk use, either in combination or separately, appear in fact to have been underlying the rather stable numerical patterns in ancient China all the way back to the late Shang dynasty (1300–1046 BCE). Bringing to light such a long-standing technique, which awaits further confirmation from the ever-growing database of newly discovered numerical and textual records, can change drastically our understanding of early Chinese history and of the historical development of sophisticated arithmetical practices and the rationalization of chance.</p></div>","PeriodicalId":50982,"journal":{"name":"Archive for History of Exact Sciences","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2019-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s00407-019-00245-9","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50467834","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
The Principia’s second law (as Newton understood it) from Galileo to Laplace 从伽利略到拉普拉斯的第二定律(牛顿的理解)
IF 0.5 2区 哲学
Archive for History of Exact Sciences Pub Date : 2019-11-26 DOI: 10.1007/s00407-019-00242-y
Bruce Pourciau
{"title":"The Principia’s second law (as Newton understood it) from Galileo to Laplace","authors":"Bruce Pourciau","doi":"10.1007/s00407-019-00242-y","DOIUrl":"10.1007/s00407-019-00242-y","url":null,"abstract":"<div><p>Newton certainly regarded his second law of motion in the <i>Principia </i>as a fundamental axiom of mechanics. Yet the works that came after the <i>Principia,</i> the major treatises on the foundations of mechanics in the eighteenth century—by Varignon, Hermann, Euler, Maclaurin, d’Alembert, Euler (again), Lagrange, and Laplace—do not record, cite, discuss, or even mention the <i>Principia</i>’s statement of the second law. Nevertheless, the present study shows that all of these scientists do in fact assume the principle that the <i>Principia</i>’s second law asserts as a fundamental axiom in their mechanics. (For what that second law asserts, we rely on Newton’s own testimony.) Some, like Varignon and Hermann, assume the axiom implicitly, apparently unaware that any assumption is being made, while others, like Maclaurin and Euler, assume the axiom explicitly, apparently unaware that the assertion assumed is the second law as Newton himself understood it. But in every case these scientists employ the principle asserted by the <i>Principia</i>’s second law <i>fundamentally</i>, unaware that they should be citing <span>Neutonus</span>, <i>Prin., Phil. Nat. Math</i>., Lex II.\u0000</p></div>","PeriodicalId":50982,"journal":{"name":"Archive for History of Exact Sciences","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2019-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s00407-019-00242-y","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42054177","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
The Jalālī Calendar: the enigma of its radix date %1（%2）其基数之谜
IF 0.5 2区 哲学
Archive for History of Exact Sciences Pub Date : 2019-11-12 DOI: 10.1007/s00407-019-00240-0
Hamid-Reza Giahi Yazdi
{"title":"The Jalālī Calendar: the enigma of its radix date","authors":"Hamid-Reza Giahi Yazdi","doi":"10.1007/s00407-019-00240-0","DOIUrl":"10.1007/s00407-019-00240-0","url":null,"abstract":"<div><p>The <i>Jalālī</i> (or <i>Malikī</i>) Calendar is well known to Iranian and Western researchers. It was established by the order of Sulṭān Jalāl al-Dīn Malikshāh-i Saljūqī in the 5th c. A.H. (The dates which are designated with A.H. indicate the <i>Hijrī</i> Calendar.)/11th c. A.D. in Isfahan. After the death of Yazdigird III (the last king of the Sassanid dynasty), the <i>Yazdigirdī</i> Calendar, as a solar one, gradually lost its position, and the <i>Hijrī</i> Calendar replaced it. After the rise of Islam, nonetheless, Iranians preferred various solar calendars to the <i>Hijrī</i> one. <i>The Jalālī</i> Calendar must be considered the culmination of such efforts. The present article deals with the riddle of the radix date (epoch) of the <i>Jalālī</i> Calendar. The author examines the problem through a historical approach and provides a novel solution to the question.</p></div>","PeriodicalId":50982,"journal":{"name":"Archive for History of Exact Sciences","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2019-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s00407-019-00240-0","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42808914","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Une controverse entre Émile Picard et Leopold Kronecker emile Picard和Leopold Kronecker之间的争论
IF 0.5 2区 哲学
Archive for History of Exact Sciences Pub Date : 2019-11-09 DOI: 10.1007/s00407-019-00241-z
Cédric Vergnerie
{"title":"Une controverse entre Émile Picard et Leopold Kronecker","authors":"Cédric Vergnerie","doi":"10.1007/s00407-019-00241-z","DOIUrl":"https://doi.org/10.1007/s00407-019-00241-z","url":null,"abstract":"","PeriodicalId":50982,"journal":{"name":"Archive for History of Exact Sciences","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2019-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s00407-019-00241-z","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"51872533","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Une controverse entre Émile Picard et Leopold Kronecker 埃米尔·皮卡德和利奥波德·克罗内克之间的争论
IF 0.5 2区 哲学
Archive for History of Exact Sciences Pub Date : 2019-11-09 DOI: 10.1007/s00407-019-00241-z
Cédric Vergnerie
{"title":"Une controverse entre Émile Picard et Leopold Kronecker","authors":"Cédric Vergnerie","doi":"10.1007/s00407-019-00241-z","DOIUrl":"10.1007/s00407-019-00241-z","url":null,"abstract":"<div><h2>Résumé</h2><div><p>Dans deux articles publiés en 1869 et 1878, Leopold Kronecker construit une théorie qui prend sa source dans le travail de Sturm sur la détermination du nombre de solutions réelles d’une équation. La présentation de cette <i>théorie des caractéristiques</i> par Émile Picard va donner lieu à une controverse entre les deux mathématiciens sur la paternité d’une formule donnant le nombre de solutions de certains systèmes de plusieurs équations. Après avoir donné un aperçu de la théorie des caractéristiques, nous montrerons comment, à travers cette dispute, c’est en fait la façon dont ces deux mathématiciens appréhendent les mathématiques qui est en jeu.</p></div></div>","PeriodicalId":50982,"journal":{"name":"Archive for History of Exact Sciences","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2019-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s00407-019-00241-z","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50466730","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
What were the genuine Banach spaces in 1922? Reflection on axiomatisation and progression of the mathematical thought 1922年真正的巴拿赫空间是什么？关于数学思想公理化和发展的思考
IF 0.5 2区 哲学
Archive for History of Exact Sciences Pub Date : 2019-10-26 DOI: 10.1007/s00407-019-00239-7
Frédéric Jaëck
{"title":"What were the genuine Banach spaces in 1922? Reflection on axiomatisation and progression of the mathematical thought","authors":"Frédéric Jaëck","doi":"10.1007/s00407-019-00239-7","DOIUrl":"10.1007/s00407-019-00239-7","url":null,"abstract":"<div><p>This paper provides an analysis of the use of axioms in Banach’s Ph.D. and their role in the progression of Banach’s mathematical thought. In order to give a precise account of the role of Banach’s axioms, we distinguish two levels of activity. The first one is devoted to the overall process of creating a new theory able to answer some prescribed problems in functional analysis. The second one concentrates on the epistemological role of axioms. In particular, the notion of norm completeness, as it appears in Banach’s text, can be interpreted as an epistemic linchpin between several a priori inhomogeneous domains of mathematical thought.</p></div>","PeriodicalId":50982,"journal":{"name":"Archive for History of Exact Sciences","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2019-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s00407-019-00239-7","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50516158","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
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