Archive for History of Exact Sciences最新文献_第7页

The Archimedean ‘sambukē’ of Damis in Biton 比顿达米斯的阿基米德“sambukı”

IF 0.5 2区哲学

Archive for History of Exact Sciences Pub Date : 2021-09-08 DOI: 10.1007/s00407-021-00281-4

Paul T. Keyser

引用次数: 0

Euler first theory of resonance 欧拉第一共振理论

IF 0.5 2区哲学

Archive for History of Exact Sciences Pub Date : 2021-07-10 DOI: 10.1007/s00407-021-00280-5

Sylvio R. Bistafa

{"title":"Euler first theory of resonance","authors":"Sylvio R. Bistafa","doi":"10.1007/s00407-021-00280-5","DOIUrl":"10.1007/s00407-021-00280-5","url":null,"abstract":"<div><p>We examine a publication by Euler, <i>De novo genere oscillationum</i>, written in 1739 and published in 1750, in which he derived for the first time, the differential equation of the (undamped) simple harmonic oscillator under harmonic excitation, namely the motion of an object acted on by two forces, one proportional to the distance traveled, the other varying sinusoidally with time. He then developed a general solution, using two different methods of integration, making extensive use of direct and inverse sine and cosine functions. After much manipulation of the resulting equations, he proceeded to an analysis of the periodicity of the solutions by varying the relation between two parameters, <span>(a)</span> and <span>(b)</span>, eventually identifying the phenomenon of resonance in the case where <span>(2b=a)</span>. This is shown to be nothing more than the equality between the driving frequency and the natural frequency of the oscillator, which, indeed, characterizes the phenomenon of resonance. Graphical representations of the behavior of the oscillator for different relations between these parameters are given. Despite having been a brilliant discovery, Euler’s publication was not influential and has been neglected by scholars and by specialized publications alike.</p></div>","PeriodicalId":50982,"journal":{"name":"Archive for History of Exact Sciences","volume":"76 3","pages":"207 - 221"},"PeriodicalIF":0.5,"publicationDate":"2021-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s00407-021-00280-5","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41587539","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

Carnot’s theory of transversals and its applications by Servois and Brianchon: the awakening of synthetic geometry in France 卡诺的横截面理论及其应用——法国合成几何的觉醒

IF 0.5 2区哲学

Archive for History of Exact Sciences Pub Date : 2021-06-08 DOI: 10.1007/s00407-021-00276-1

Andrea Del Centina

引用次数: 4

Vitali’s generalized absolute differential calculus Vitali的广义绝对微分学

IF 0.5 2区哲学

Archive for History of Exact Sciences Pub Date : 2021-05-24 DOI: 10.1007/s00407-021-00273-4

Alberto Cogliati

引用次数: 1

An alternative interpretation of BM 76829: astrological schemes for length of life and parts of the body BM 76829的另一种解释：寿命和身体部位的占星术方案

IF 0.5 2区哲学

Archive for History of Exact Sciences Pub Date : 2021-05-20 DOI: 10.1007/s00407-021-00279-y

John Steele

引用次数: 0

Mathématiques en perspective: Desargues, la Hire, le Poîvre 透视数学:Desargues, la Hire, le poivre

IF 0.5 2区哲学

Archive for History of Exact Sciences Pub Date : 2021-05-18 DOI: 10.1007/s00407-021-00275-2

Jean-Yves Briend

引用次数: 1

David Hilbert and the foundations of the theory of plane area 大卫·希尔伯特和平面面积理论的基础

IF 0.5 2区哲学

Archive for History of Exact Sciences Pub Date : 2021-05-05 DOI: 10.1007/s00407-021-00278-z

Eduardo N. Giovannini

引用次数: 2

Fiction, possibility and impossibility: three kinds of mathematical fictions in Leibniz’s work 虚构、可能与不可能：莱布尼茨作品中的三种数学小说

IF 0.5 2区哲学

Archive for History of Exact Sciences Pub Date : 2021-04-24 DOI: 10.1007/s00407-021-00277-0

Oscar M. Esquisabel, Federico Raffo Quintana

{"title":"Fiction, possibility and impossibility: three kinds of mathematical fictions in Leibniz’s work","authors":"Oscar M. Esquisabel, Federico Raffo Quintana","doi":"10.1007/s00407-021-00277-0","DOIUrl":"10.1007/s00407-021-00277-0","url":null,"abstract":"<div><p>This paper is concerned with the status of mathematical fictions in Leibniz’s work and especially with infinitary quantities as fictions. Thus, it is maintained that mathematical fictions constitute a kind of symbolic notion that implies various degrees of impossibility. With this framework, different kinds of notions of possibility and impossibility are proposed, reviewing the usual interpretation of both modal concepts, which appeals to the consistency property. Thus, three concepts of the possibility/impossibility pair are distinguished; they give rise, in turn, to three concepts of mathematical fictions. Moreover, such a distinction is the base for the claim that infinitesimal quantities, as mathematical fictions, do not imply an absolute impossibility, resulting from self-contradiction, but a relative impossibility, founded on irrepresentability and on the fact that it does not conform to architectural principles. In conclusion, this “soft” impossibility of infinitesimals yields them, in Leibniz view, a presumptive or “conjectural” status.</p></div>","PeriodicalId":50982,"journal":{"name":"Archive for History of Exact Sciences","volume":"75 6","pages":"613 - 647"},"PeriodicalIF":0.5,"publicationDate":"2021-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s00407-021-00277-0","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43936314","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: 5

The six books of Diophantus’ Arithmetic increased and reduced to specious: the lost manuscript of Jacques Ozanam (1640–1718) 丢番图《算术》的六卷书增加了又减少了，变得似是而非:雅克·奥扎南(1640-1718)丢失的手稿

IF 0.5 2区哲学

Archive for History of Exact Sciences Pub Date : 2021-04-13 DOI: 10.1007/s00407-021-00274-3

Francisco Gómez-García, Pedro J. Herrero-Piñeyro, Antonio Linero-Bas, Ma. Rosa Massa-Esteve, Antonio Mellado-Romero

{"title":"The six books of Diophantus’ Arithmetic increased and reduced to specious: the lost manuscript of Jacques Ozanam (1640–1718)","authors":"Francisco Gómez-García, Pedro J. Herrero-Piñeyro, Antonio Linero-Bas, Ma. Rosa Massa-Esteve, Antonio Mellado-Romero","doi":"10.1007/s00407-021-00274-3","DOIUrl":"10.1007/s00407-021-00274-3","url":null,"abstract":"<div><p>The introduction of a new analytical method, due fundamentally to François Viète and René Descartes and the later dissemination of their works, resulted in a profound change in the way of thinking and doing mathematics. This change, known as process of algebrization, occurred during the seventeenth and early eighteenth centuries and led to a great transformation in mathematics. Among many other consequences, this process gave rise to the treatment of the results in the classic treatises with the new analytical method, which allowed new visions of such treatises and the obtaining of new results. Among those treatises is the <i>Arithmetic</i> of Diophantus of Alexandria (approx. 200–284) which was written, using the new algebraic language, by the French mathematician Jacques Ozanam (1640–1718), who in addition to profusely increasing the original problems of Diophantus, solved them in a general way, thus obtaining many geometric consequences. The work is handwritten, it has never been published, it has been lost for almost 300 years, and the known references show its importance. We will show that Ozanam’s manuscript was quoted as an important work on several occasions by others mathematicians of the time, among whom G. W. Leibniz stands out. Once the manuscript has been located, our aim in this article is to show and analyze this work of Ozanam, its content, its notation and its structure and how, through the new algebraic method, he not only solved and expanded the questions proposed by Diophantus, but also introduced a connection between the algebraic solutions and what he called geometric determinations by obtaining loci from the solutions.\u0000</p></div>","PeriodicalId":50982,"journal":{"name":"Archive for History of Exact Sciences","volume":"75 5","pages":"557 - 611"},"PeriodicalIF":0.5,"publicationDate":"2021-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s00407-021-00274-3","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43160884","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

A study of Babylonian records of planetary stations 对巴比伦行星站记录的研究

IF 0.5 2区哲学

Archive for History of Exact Sciences Pub Date : 2021-02-18 DOI: 10.1007/s00407-021-00272-5

J. M. Steele, E. L. Meszaros

{"title":"A study of Babylonian records of planetary stations","authors":"J. M. Steele, E. L. Meszaros","doi":"10.1007/s00407-021-00272-5","DOIUrl":"10.1007/s00407-021-00272-5","url":null,"abstract":"<div><p>Late Babylonian astronomical texts contain records of the stationary points of the outer planets using three different notational formats: Type S where the position is given relative to a Normal Star and whether it is an eastern or western station is noted, Type I which is similar to Type S except that the Normal Star is replaced by a reference to a zodiacal sign, and Type Z the position is given by reference to a zodiacal sign, but no indication of whether the station is an eastern or western station is included. In these records, the date of the station is sometimes preceded by the terms <i>in</i> and/or EN. We have created a database of station records in order to determine whether there was any pattern in the use of these notation types over time or an association with any bias in the station date or the type of text the station was recorded in. Predictive texts, which include Almanacs and Normal Star Almanacs, almost always use Type Z notation, while the Diaries, compilations, and Goal-Year Texts use all three types. Type Z records almost never include <i>in</i> or EN, while other types seem to include these interchangeably. When compared with modern computed station dates, the records show bias toward earlier dates, suggesting that the Babylonians were observing dates when the planets appeared to stop moving rather than the true station. Overlapping reports, where a station on the same date was recorded in two or more texts, suggest that predicted station dates were used to guide observations, and that the planet’s position on the predicted stationary date was the true point of the observation rather than the specific date of the stationary point.</p></div>","PeriodicalId":50982,"journal":{"name":"Archive for History of Exact Sciences","volume":"75 4","pages":"415 - 438"},"PeriodicalIF":0.5,"publicationDate":"2021-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s00407-021-00272-5","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44676940","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