Archive for History of Exact Sciences最新文献_第10页

Pascal’s mystic hexagram, and a conjectural restoration of his lost treatise on conic sections 帕斯卡神秘的六进制，以及他遗失的圆锥曲线论文的推测性恢复

IF 0.5 2区哲学

Archive for History of Exact Sciences Pub Date : 2020-07-08 DOI: 10.1007/s00407-020-00251-2

Andrea Del Centina

引用次数: 8

Polygons of Petrović and Fine, algebraic ODEs, and contemporary mathematics Petrović和Fine的多边形、代数常微分方程和当代数学

IF 0.5 2区哲学

Archive for History of Exact Sciences Pub Date : 2020-06-29 DOI: 10.1007/s00407-020-00250-3

Vladimir Dragović, Irina Goryuchkina

引用次数: 3

Mathématiques et architecture: le tracé de l’entasis par Nicolas-François Blondel 数学与建筑：Nicolas François Blondel的图

IF 0.5 2区哲学

Archive for History of Exact Sciences Pub Date : 2020-04-23 DOI: 10.1007/s00407-020-00248-x

Dominique Raynaud

{"title":"Mathématiques et architecture: le tracé de l’entasis par Nicolas-François Blondel","authors":"Dominique Raynaud","doi":"10.1007/s00407-020-00248-x","DOIUrl":"10.1007/s00407-020-00248-x","url":null,"abstract":"<div><p>In <i>Résolution des quatre principaux problèmes d’architecture</i> (1673) then in <i>Cours d’architecture</i> (1683), the architect–mathematician Nicolas-François Blondel addresses one of the most famous architectural problems of all times, that of the reduction in columns (<i>entasis</i>). The interest of the text lies in the variety of subjects that are linked to this issue. (1) The text is a response to the challenge launched by Curabelle in 1664 under the name <i>Étrenne à tous les architectes</i>; (2) Blondel mathematicizes the problem in the “style of the Ancients”; (3) The problem is reformulated and solved through the continuous drawing of the curve; (4) Blondel refutes the uniqueness of the curve by enumerating a variety of solutions (conchoid, spiral, parabola, ellipse, circle, hyperbola). This exuberance responds to an intention that does not coincide with the state of the art of mathematics at the end of the seventeenth century, nor with the taste for geometry of the Ancients, nor with any pedagogical project. This feature is explained by Blondel’s plan to found architecture on scientific bases. The reasons for his failure are analysed.</p></div>","PeriodicalId":50982,"journal":{"name":"Archive for History of Exact Sciences","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2020-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s00407-020-00248-x","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41707604","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: 4

Leibniz’s syncategorematic infinitesimals II: their existence, their use and their role in the justification of the differential calculus 莱布尼茨的合范畴无穷小Ⅱ：它们的存在、使用及其在微分学论证中的作用

IF 0.5 2区哲学

Archive for History of Exact Sciences Pub Date : 2020-04-06 DOI: 10.1007/s00407-020-00249-w

David Rabouin, Richard T. W. Arthur

{"title":"Leibniz’s syncategorematic infinitesimals II: their existence, their use and their role in the justification of the differential calculus","authors":"David Rabouin, Richard T. W. Arthur","doi":"10.1007/s00407-020-00249-w","DOIUrl":"10.1007/s00407-020-00249-w","url":null,"abstract":"<div><p>In this paper, we endeavour to give a historically accurate presentation of how Leibniz understood his infinitesimals, and how he justified their use. Some authors claim that when Leibniz called them “fictions” in response to the criticisms of the calculus by Rolle and others at the turn of the century, he had in mind a different meaning of “fiction” than in his earlier work, involving a commitment to their existence as non-Archimedean elements of the continuum. Against this, we show that by 1676 Leibniz had already developed an interpretation from which he never wavered, according to which infinitesimals, like infinite wholes, cannot be regarded as existing because their concepts entail contradictions, even though they may be used as if they exist under certain specified conditions—a conception he later characterized as “syncategorematic”. Thus, one cannot infer the <i>existence</i> of infinitesimals from their successful <i>use</i>. By a detailed analysis of Leibniz’s arguments in his <i>De quadratura</i> of 1675–1676, we show that Leibniz had already presented there two strategies for presenting infinitesimalist methods, one in which one uses finite quantities that can be made as small as necessary in order for the error to be smaller than can be assigned, and thus zero; and another “direct” method in which the infinite and infinitely small are introduced by a fiction analogous to imaginary roots in algebra, and to points at infinity in projective geometry. We then show how in his mature papers the latter strategy, now articulated as based on the Law of Continuity, is presented to critics of the calculus as being equally constitutive for the foundations of algebra and geometry and also as being provably rigorous according to the accepted standards in keeping with the Archimedean axiom.</p></div>","PeriodicalId":50982,"journal":{"name":"Archive for History of Exact Sciences","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2020-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s00407-020-00249-w","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45467689","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: 11

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

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

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

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, 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