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Gauss on least-squares and maximum-likelihood estimation 最小二乘上的高斯和最大似然估计
IF 0.5 2区 哲学
Archive for History of Exact Sciences Pub Date : 2022-04-02 DOI: 10.2139/ssrn.3990758
J. Magnus
{"title":"Gauss on least-squares and maximum-likelihood estimation","authors":"J. Magnus","doi":"10.2139/ssrn.3990758","DOIUrl":"https://doi.org/10.2139/ssrn.3990758","url":null,"abstract":"Gauss’ 1809 discussion of least squares, which can be viewed as the beginning of mathematical statistics, is reviewed. The general consensus seems to be that Gauss’ arguments are at fault, but we show that his reasoning is in fact correct, given his self-imposed restrictions, and persuasive without these restrictions.","PeriodicalId":50982,"journal":{"name":"Archive for History of Exact Sciences","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44611517","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
Gauss on least-squares and maximum-likelihood estimation 最小二乘上的高斯和最大似然估计
IF 0.5 2区 哲学
Archive for History of Exact Sciences Pub Date : 2022-04-02 DOI: 10.1007/s00407-022-00291-w
Jan R. Magnus
{"title":"Gauss on least-squares and maximum-likelihood estimation","authors":"Jan R. Magnus","doi":"10.1007/s00407-022-00291-w","DOIUrl":"10.1007/s00407-022-00291-w","url":null,"abstract":"<div><p>Gauss’ 1809 discussion of least squares, which can be viewed as the beginning of mathematical statistics, is reviewed. The general consensus seems to be that Gauss’ arguments are at fault, but we show that his reasoning is in fact correct, given his self-imposed restrictions, and persuasive without these restrictions.</p></div>","PeriodicalId":50982,"journal":{"name":"Archive for History of Exact Sciences","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00407-022-00291-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43950508","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Brianchon and Poncelet’s joint memoir, the nine-point circle, and beyond 布里安松和庞塞莱的联合回忆录《九点圆》以及其他
IF 0.5 2区 哲学
Archive for History of Exact Sciences Pub Date : 2022-03-08 DOI: 10.1007/s00407-022-00286-7
Andrea Del Centina
{"title":"Brianchon and Poncelet’s joint memoir, the nine-point circle, and beyond","authors":"Andrea Del Centina","doi":"10.1007/s00407-022-00286-7","DOIUrl":"10.1007/s00407-022-00286-7","url":null,"abstract":"<div><p>In this paper, we give a thorough account of Brianchon and Poncelet’s joint memoir on equilateral hyperbolas subject to four given conditions, focusing on the most significant theorems expounded therein, and the determination of the “nine-point circle”. We also discuss about the origin of this very rare example of collaborative work for the time, and the general challenge of finding the nature of the loci described by the centres of the conic sections required to pass through <i>m</i> points and to be tangent to <i>n</i> straight lines given in position, <i>m</i> + <i>n</i> = 4, which was posed at the end of their work. In the case <i>m</i> = 4, i.e. when the conic sections have to pass through the vertices of a quadrilateral, the locus of centres is another conic section passing through the intersection points of the opposite sides and the two diagonals of the quadrilateral, respectively, and, as Gergonne showed analytically shortly after, through other significant points connected with the quadrilateral; this curve was later given the name of the “nine-point conic”, being a natural generalization of the above mentioned circle.</p></div>","PeriodicalId":50982,"journal":{"name":"Archive for History of Exact Sciences","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00407-022-00286-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45791191","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A common-sense approach to the problem of the itinerary stadion 解决行程站问题的常识性方法
IF 0.5 2区 哲学
Archive for History of Exact Sciences Pub Date : 2022-03-03 DOI: 10.1007/s00407-022-00287-6
Irina Tupikova
{"title":"A common-sense approach to the problem of the itinerary stadion","authors":"Irina Tupikova","doi":"10.1007/s00407-022-00287-6","DOIUrl":"10.1007/s00407-022-00287-6","url":null,"abstract":"<div><p>Estimating the length of the Greek stadion remains controversial. This paper highlights the pitfalls of a purely metrological approach to this problem and proposes a formal differentiation between metrologically defined ancient measuring units and other measures used to estimate long distances. The common-sense approach to the problem is strengthened by some cross-over documentary evidence for usage of the so-called <i>itinerary</i> stadion in antiquity. We discuss the possibility of using statistical analysis methods to estimate the length of the stadion by comparing ancient routes with the actual distances. Simple numerical examples explain the limits of this approach, caused by the low number of data and by their mixed character. A special case of distances which can be calculated with the help of coordinates given in Ptolemy’s <i>Geography</i> is discussed, and has been shown to lead unavoidably to ambiguous solutions.</p></div>","PeriodicalId":50982,"journal":{"name":"Archive for History of Exact Sciences","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00407-022-00287-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44351084","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Peirce’s Dragon-Head Logic (R 501, 1901) 皮尔斯龙头逻辑(r501, 1901)
IF 0.5 2区 哲学
Archive for History of Exact Sciences Pub Date : 2022-02-24 DOI: 10.1007/s00407-021-00285-0
Minghui Ma, Ahti-Veikko Pietarinen
{"title":"Peirce’s Dragon-Head Logic (R 501, 1901)","authors":"Minghui Ma,&nbsp;Ahti-Veikko Pietarinen","doi":"10.1007/s00407-021-00285-0","DOIUrl":"10.1007/s00407-021-00285-0","url":null,"abstract":"<div><p>Peirce wrote in late 1901 a text on formal logic using a special Dragon-Head and Dragon-Tail notation in order to express the relation of logical consequence and its properties. These texts have not been referred to in the literature before. We provide a complete reconstruction and transcription of these previously unpublished sets of manuscript sheets and analyse their main content. In the reconstructed text, Peirce is seen to outline both a general theory of deduction and a general theory of consequence relation. The two are the cornerstones of modern logic and have played a crucial role in its development. From the wider perspective, Peirce is led to these theories by three important generalizations: propositions to all signs, truth to scriptibility, and derivation to transformability. We provide an exposition of such proposed semiotic foundation for logical constants and point out a couple of further innovations in this rare text, including the sheet of assertion, correction as a dual of deduction and the nature of conditionals as variably strict conditionals.</p></div>","PeriodicalId":50982,"journal":{"name":"Archive for History of Exact Sciences","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43276321","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
Federico Commandino and the Latin edition of Pappus’ Collection Federico Commandino与Pappus文集拉丁版
IF 0.5 2区 哲学
Archive for History of Exact Sciences Pub Date : 2021-11-21 DOI: 10.1007/s00407-021-00284-1
Argante Ciocci
{"title":"Federico Commandino and the Latin edition of Pappus’ Collection","authors":"Argante Ciocci","doi":"10.1007/s00407-021-00284-1","DOIUrl":"10.1007/s00407-021-00284-1","url":null,"abstract":"<div><p>The Latin edition of the <i>Mathematicae Collectiones</i> was published in print in 1588, thirteen years after Federico Commandino’s demise. For his Latin version of Pappus’s work, Comandino used two Greek codices, formerly identified by Treweek. In this article, another Greek manuscript, revised and annotated by Commandino, is revealed. Two letters from Commandino to Ettore Ausonio shed new light on the edition of Pappus’s <i>Collectio</i> and show the partnership between the two mathematicians in elaborating supplementary proofs to include in the comments. Using these letters, we can date the first draft of the Latin version in the late 1560s. The posthumous edition of the <i>Mathematicae Collectiones</i> involved Commandino’s disciples and, in particular, Guidobaldo del Monte. The comparison between the manuscripts and the printed edition reveals an important role played by the disciple in revising the Latin translation of his master.</p></div>","PeriodicalId":50982,"journal":{"name":"Archive for History of Exact Sciences","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43391478","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
Poincaré’s works leading to the Poincaré conjecture 庞加莱的作品引出了庞加莱猜想
IF 0.5 2区 哲学
Archive for History of Exact Sciences Pub Date : 2021-10-13 DOI: 10.1007/s00407-021-00283-2
Lizhen Ji, Chang Wang
{"title":"Poincaré’s works leading to the Poincaré conjecture","authors":"Lizhen Ji,&nbsp;Chang Wang","doi":"10.1007/s00407-021-00283-2","DOIUrl":"10.1007/s00407-021-00283-2","url":null,"abstract":"<div><p>In the last decade, the Poincaré conjecture has probably been the most famous statement among all the contributions of Poincaré to the mathematics community. There have been many papers and books that describe various attempts and the final works of Perelman leading to a positive solution to the conjecture, but the evolution of Poincaré’s works leading to this conjecture has not been carefully discussed or described, and some other historical aspects about it have not been addressed either. For example, one question is how it fits into the overall work of Poincaré in topology, and what are some other related questions that he had raised. Since Poincaré did not state the Poincaré conjecture as a conjecture but rather raised it as a question, one natural question is why he did this. In order to address these issues, in this paper, we examine Poincaré’s works in topology in the framework of classifying manifolds through numerical and algebraic invariants. Consequently, we also provide a full history of the formulation of the Poincaré conjecture which is richer than what is usually described and accepted and hence gain a better understanding of overall works of Poincaré in topology. In addition, this analysis clarifies a puzzling question on the relation between Poincaré’s stated motivations for topology and the Poincaré conjecture.</p></div>","PeriodicalId":50982,"journal":{"name":"Archive for History of Exact Sciences","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48943513","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
Nombrils, bruslans, autrement foyerz: la géométrie projective en action dans le Brouillon Project de Girard Desargues Nombrils，Bruslans，Autrement Foyerz:Girard Desargues的Brouillon项目中的投影几何
IF 0.5 2区 哲学
Archive for History of Exact Sciences Pub Date : 2021-09-16 DOI: 10.1007/s00407-021-00282-3
Marie Anglade, Jean-Yves Briend
{"title":"Nombrils, bruslans, autrement foyerz: la géométrie projective en action dans le Brouillon Project de Girard Desargues","authors":"Marie Anglade,&nbsp;Jean-Yves Briend","doi":"10.1007/s00407-021-00282-3","DOIUrl":"10.1007/s00407-021-00282-3","url":null,"abstract":"<div><p>In the middle part of his <i>Brouillon Project</i> on conics, Girard Desargues develops the theory of the <i>traversale</i>, a notion that generalizes the Apollonian diameter and allows to give a unified treatment of the three kinds of conics. We showed elsewhere that it leads Desargues to a complete theory of projective polarity for conics. The present article, which shall close our study of the <i>Brouillon Project</i>, is devoted to the last part of the text, in which Desargues puts his theory of the traversal into practice by giving a very elegant tratment of the classical theory of parameters and foci. This will lead us to show that Desargues’ proofs can only be understood if one accepts that he reasons in a resolutely projective framework, completely assimilating elements at infinity to those at finite distance in his proofs.</p></div>","PeriodicalId":50982,"journal":{"name":"Archive for History of Exact Sciences","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00407-021-00282-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50488763","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
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
{"title":"The Archimedean ‘sambukē’ of Damis in Biton","authors":"Paul T. Keyser","doi":"10.1007/s00407-021-00281-4","DOIUrl":"10.1007/s00407-021-00281-4","url":null,"abstract":"<div><p>Biton’s <i>Construction of Machines of War and Catapults</i> describes six machines by five engineers or inventors; the fourth machine is a rolling elevatable scaling ladder, named <i>sambukē</i>, designed by one Damis of Kolophōn. The first <i>sambukē</i> was invented by Herakleides of Taras, in 214 BCE, for the Roman siege of Syracuse. Biton is often dismissed as incomprehensible or preposterous. I here argue that the account of Damis’ device is largely coherent and shows that Biton understood that Damis had built a machine that embodied Archimedean principles. The machine embodies three such principles: (1) the proportionate balancing of the torques on a lever (from <i>Plane Equilibria</i>, an early work); (2) the concept of specific gravity or density (from <i>Floating Bodies</i>, a late work); and (3) the κοχλίας, i.e., a worm drive (invented <i>ca</i> 240 BCE), with the toothed wheel functioning as the horizontal axis of rotation of the elevated ladder. Moreover, the stone-thrower of Isidoros of Abydos (the second machine in Biton) also embodies the κοχλίας.</p></div>","PeriodicalId":50982,"journal":{"name":"Archive for History of Exact Sciences","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2021-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44946919","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
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":null,"pages":null},"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
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