Archive for History of Exact Sciences最新文献

{"title":"Francesco Fontana (1580–1656) from practice to rules of calculation of lens systems","authors":"Yaakov Zik,&nbsp;Giora Hon","doi":"10.1007/s00407-023-00321-1","DOIUrl":"10.1007/s00407-023-00321-1","url":null,"abstract":"<div><p>In 1646, Francesco Fontana (1580–1656) published his <i>Novae Coelestium Terresriumque Rerum Observationes</i> which includes discussions of optical properties of systems of lenses, e.g., telescope and microscope. Our study of the <i>Novae Coelestium</i> shows that the advance Fontana made in optics could not have been accomplished on the basis of the traditional spectacle optics which was the dominant practice at his time. Though spectacle and telescope making share the same optical elements, improving eyesight and constructing telescope are different practices based on different principles. The production of powerful astronomical telescopes demanded objective lenses with much longer focal length and eyepiece lenses with much shorter focal length than the range of focal length of lenses used for spectacles, respectively. Moreover, higher standard of precision and purity of the glass was required. The transition from the practice by which optical components were chosen from ready-made spectacle lenses to lenses which were produced according to predetermined specifications (e.g., calculation of focal length) was anything but straight forward. We argue that Fontana developed the optical knowledge necessary for improving the performance of optical systems. Essentially, he formulated—based on rich practical experience—a set of rules of calculation by which optical properties of a lens system could be determined and adjusted as required.</p></div>","PeriodicalId":50982,"journal":{"name":"Archive for History of Exact Sciences","volume":"78 2","pages":"153 - 182"},"PeriodicalIF":0.7,"publicationDate":"2023-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134953415","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}

{"title":"The efflux problem: how hydraulics became divorced from hydrodynamics","authors":"Michael Eckert","doi":"10.1007/s00407-023-00320-2","DOIUrl":"10.1007/s00407-023-00320-2","url":null,"abstract":"<div><p>The efflux problem deals with the outflow of water through an orifice in a vessel, the flow over the crest of a weir and some other ways of discharge. The difficulties to account for such fluid motions in terms of a mathematical theory made it a notorious problem throughout the history of hydraulics and hydrodynamics. The treatment of the efflux problem, therefore, reflects the diverging routes along which hydraulics became an engineering science and hydrodynamics a theoretical science out of touch with applications. By the twentieth century, the presentation of the efflux problem in textbooks on hydraulics had almost nothing in common with that in textbooks on hydrodynamics.</p></div>","PeriodicalId":50982,"journal":{"name":"Archive for History of Exact Sciences","volume":"78 2","pages":"127 - 152"},"PeriodicalIF":0.7,"publicationDate":"2023-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00407-023-00320-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135475874","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}

{"title":"Levi-Civita simplifies Einstein. The Ricci rotation coefficients and unified field theories","authors":"Franco Cardin,&nbsp;Rossana Tazzioli","doi":"10.1007/s00407-023-00322-0","DOIUrl":"10.1007/s00407-023-00322-0","url":null,"abstract":"<div><p>This paper concerns late 1920 s attempts to construct unitary theories of gravity and electromagnetism. A first attempt using a non-standard connection—with torsion and zero-curvature—was carried out by Albert Einstein in a number of publications that appeared between 1928 and 1931. In 1929, Tullio Levi-Civita discussed Einstein’s geometric structure and deduced a new system of differential equations in a Riemannian manifold endowed with what is nowadays known as Levi-Civita connection. He attained an important result: Maxwell’s electromagnetic equations and the gravitational equations were obtained exactly, while Einstein had deduced them only as a first order approximation. A main feature of Levi-Civita’s theory is the essential use of the <i>Ricci’s rotation coefficients</i>, introduced by Gregorio Ricci Curbastro many years before. We trace the history of Ricci’s coefficients that are still used today, and highlight their geometric and mechanical meaning.</p></div>","PeriodicalId":50982,"journal":{"name":"Archive for History of Exact Sciences","volume":"78 1","pages":"87 - 126"},"PeriodicalIF":0.7,"publicationDate":"2023-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135218788","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}

{"title":"Tables for the radii of the Sun, the Moon, and the shadow from John of Gmunden to Longomontanus","authors":"Bernard R. Goldstein,&nbsp;José Chabás","doi":"10.1007/s00407-023-00318-w","DOIUrl":"10.1007/s00407-023-00318-w","url":null,"abstract":"<div><p>A table in five columns for the radii of the Sun, the Moon, and the shadow is included in sets of astronomical tables from the fifteenth to the early seventeenth century, specifically in those by John of Gmunden (d. 1442), Peurbach (d. 1461), the second edition of the Alfonsine Tables (1492), Copernicus (d. 1543), Brahe (d. 1601), and Longomontanus (d. 1647). The arrangement is the same and the entries did not change much, despite many innovations in astronomical theories in this time period. In other words, there is continuity in presentation and, from the point of view of the user of these tables, changes in the theory played no role. In general, the methods for computing the entries are not described and have to be reconstructed. In this paper, we focus on the users of these tables rather than on their compilers, but we refer to modern reconstructions where appropriate. A key issue is the treatment of the size of the Moon during a solar eclipse which was not properly understood by Tycho Brahe. Kepler’s solution and that of his predecessor, Levi ben Gerson (d. 1344), are discussed.</p></div>","PeriodicalId":50982,"journal":{"name":"Archive for History of Exact Sciences","volume":"78 1","pages":"67 - 86"},"PeriodicalIF":0.7,"publicationDate":"2023-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134886782","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}

{"title":"Geographic longitude in Latin Europe during the twelfth and thirteenth centuries","authors":"C. Philipp E. Nothaft","doi":"10.1007/s00407-023-00316-y","DOIUrl":"10.1007/s00407-023-00316-y","url":null,"abstract":"<div><p>This article surveys surviving evidence for the determination of geographic longitude in Latin Europe in the period between 1100 and 1300. Special consideration is given to the different types of sources that preserve longitude estimates as well as to the techniques that were used in establishing them. While the method of inferring longitude differences from eclipse times was evidently in use as early as the mid-twelfth century, it remains doubtful that it can account for most of the preserved longitudes. An analysis of 89 different estimates for 30 European cities indicates a high degree of accuracy among the longitudes of English cities and a conspicuous displacement eastward (by 5°–7;30°) shared by most longitudes of cities in Italy and France. In both cases, the data suggest a high level of interdependence between estimates for different cities in the same geographic region, although the means by which these estimates were arrived at remain insufficiently known.</p></div>","PeriodicalId":50982,"journal":{"name":"Archive for History of Exact Sciences","volume":"78 1","pages":"29 - 65"},"PeriodicalIF":0.7,"publicationDate":"2023-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00407-023-00316-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135741388","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}

{"title":"Galois and the simple group of order 60","authors":"Ian Stewart","doi":"10.1007/s00407-023-00319-9","DOIUrl":"10.1007/s00407-023-00319-9","url":null,"abstract":"<div><p>In his testamentary letter to Auguste Chevalier, Évariste Galois states that, in modern terminology, the smallest simple group has order 60. No proof of this statement survives in his papers, and it has been suggested that a proof would have been impossible using the methods available at the time. We argue that this assertion is unduly pessimistic. Moreover, one fragmentary document, dismissed as a triviality and misunderstood, looks suspiciously like cryptic notes related to this result. We give an elementary proof of Galois’s statement, explain why it is likely that he would have been aware of the methods involved, and discuss the potential relevance of the fragment.</p></div>","PeriodicalId":50982,"journal":{"name":"Archive for History of Exact Sciences","volume":"78 1","pages":"1 - 28"},"PeriodicalIF":0.7,"publicationDate":"2023-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42449957","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}

{"title":"The Helmholtz legacy in color metrics: Schrödinger’s color theory","authors":"Valentina Roberti,&nbsp;Giulio Peruzzi","doi":"10.1007/s00407-023-00317-x","DOIUrl":"10.1007/s00407-023-00317-x","url":null,"abstract":"<div><p>This study is a continuation of the authors’ previous work entitled “Helmholtz and the geometry of color space: gestation and development of Helmholtz’s line element” (Peruzzi and Roberti in Arch Hist Exact Sci. https://doi.org/10.1007/s00407-023-00304-2, 2023), which provides an account of the first metrically significant model of color space proposed by the German polymath Hermann von Helmholtz in 1891–1892. Helmholtz’s Riemannian line element for three-dimensional color space laid the foundation for all subsequent studies in the field of color metrics, although it was largely forgotten for almost three decades from the time of its first publication. The rediscovery of Helmholtz’s masterful work was due to one of the founders of quantum mechanics, Erwin Schrödinger. He established his color metric in three extended papers submitted in 1920 to the <i>Annalen der Physik</i>. Two memoirs were devoted to the so-called <i>lower color metric,</i> which laid the basis for the development of his <i>higher color metric</i>, exposed in the last paper. Schrödinger’s approach to the geometry of color space has been taken as a starting point for future elaborations of color metrics and allows a close examination of the current assumptions about the analysis of color-matching data. This paper presents an overall picture of Schrödinger’s works on color. His color theory developed a tradition first inaugurated by Newton and Young, and which acquired strong scientific ground with Grassmann’s, Maxwell’s, and Helmholtz’s contributions in the 1850s. Special focus will be given to Schrödinger’s account of color metric, which responded directly to Helmholtz’s hypothesis of a Riemannian line element for color space.</p></div>","PeriodicalId":50982,"journal":{"name":"Archive for History of Exact Sciences","volume":"77 6","pages":"615 - 635"},"PeriodicalIF":0.5,"publicationDate":"2023-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00407-023-00317-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44325982","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}

{"title":"Hero and the tradition of the circle segment","authors":"Henry Mendell","doi":"10.1007/s00407-023-00308-y","DOIUrl":"10.1007/s00407-023-00308-y","url":null,"abstract":"<div><p>In his <i>Metrica</i>, Hero provides four procedures for finding the area of a circular segment (with <i>b</i> the base of the segment and <i>h</i> its height): an Ancient method for when the segment is smaller than a semicircle, <span>((b + h)/2 , cdot , h)</span>; a Revision, <span>((b + h)/2 , cdot , h + (b/2)^{2} /14)</span>; a quasi-Archimedean method (said to be inspired by the quadrature of the parabola) for cases where <i>b</i> is more than triple <i>h</i>, <span>({raise0.5exhbox{$scriptstyle 4$} kern-0.1em/kern-0.15em lower0.25exhbox{$scriptstyle 3$}}(h , cdot , b/2))</span>; and a method of Subtraction using the Revised method, for when it is larger than a semicircle. He gives superficial arguments that the Ancient method presumes <span>(pi = 3)</span> and the Revision, <span>(pi = {raise0.5exhbox{$scriptstyle {22}$} kern-0.1em/kern-0.15em lower0.25exhbox{$scriptstyle 7$}})</span>. We are left with many questions. How ancient is the Ancient? Why did anyone think it worked? Why would anyone revise it in just this way? In addition, why did Hero think the Revised method did not work when <span>(b &gt; 3;h)</span>? I show that a fifth century BCE Uruk tablet employs the Ancient method, but possibly with very strange consequences, and that a Ptolemaic Egyptian papyrus that checks this method by comparing the area of a circle calculated from the sum of a regular inscribed polygon and the areas of the segments on its sides as determined by the Ancient method with the area of the circle as calculated from its diameter correctly sees that the calculations do not quite gel in the case of a triangle but do in the case of a square. Both traditions probably could also calculate the area of a segment on an inscribed regular polygon by subtracting the area of the polygon from the area of the circle and dividing by the number of sides of the polygon. I then derive two theorems about pairs of segments, that the reviser of the Ancient method should have known, that explain each method, why they work when they do and do not when they do not, and which lead to a curious generalization of the Revised method. Hero’s comment is right, but not for the reasons he gives. I conclude with an exploration of Hero’s restrictions of the Revised method and Hero’s two alternative methods.</p></div>","PeriodicalId":50982,"journal":{"name":"Archive for History of Exact Sciences","volume":"77 5","pages":"451 - 499"},"PeriodicalIF":0.5,"publicationDate":"2023-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00407-023-00308-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41439424","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}

{"title":"Auerbach, Lotka, and Zipf: pioneers of power-law city-size distributions","authors":"Diego Rybski,&nbsp;Antonio Ciccone","doi":"10.1007/s00407-023-00314-0","DOIUrl":"10.1007/s00407-023-00314-0","url":null,"abstract":"<div><p>Power-law city-size distributions are a statistical regularity researched in many countries and urban systems. In this history of science treatise we reconsider Felix Auerbach’s paper published in 1913. We reviewed his analysis and found (i) that a constant absolute concentration, as introduced by him, is equivalent to a power-law distribution with exponent <span>(approx 1)</span>, (ii) that Auerbach describes this equivalence, and (iii) that Auerbach also pioneered the empirical analysis of city-size distributions across countries, regions, and time periods. We further investigate his legacy as reflected in citations and find that important follow-up work, e.g. by Lotka (Elements of physical biology. Williams &amp; Wilkins Company, Baltimore, 1925) and Zipf (Human behavior and the principle of least effort: an introduction to human ecology, Martino Publishing, Manfield Centre, CT (2012), 1949), does give proper reference to his discovery—but others do not. For example, only approximately 20% of city-related works citing Zipf (1949) also cite Auerbach (Petermanns Geogr Mitteilungen 59(74):74–76, 1913). To our best knowledge, Lotka (1925) was the first to describe the power-law rank-size rule as it is analyzed today. Saibante (Metron Rivista Internazionale di Statistica 7(2):53–99, 1928), building on Auerbach and Lotka, investigated the power-law rank-size rule across countries, regions, and time periods. Zipf’s achievement was to embed these findings in his monumental 1949 book. We suggest that the use of “Auerbach–Lotka–Zipf law” (or “ALZ-law”) is more appropriate than “Zipf’s law for cities”, which also avoids confusion with Zipf’s law for word frequency. We end the treatise with biographical notes on Auerbach.</p></div>","PeriodicalId":50982,"journal":{"name":"Archive for History of Exact Sciences","volume":"77 6","pages":"601 - 613"},"PeriodicalIF":0.5,"publicationDate":"2023-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00407-023-00314-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47063522","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}

{"title":"An early system A-type scheme for Saturn from Babylon","authors":"John Steele,&nbsp;Teije de Jong","doi":"10.1007/s00407-023-00311-3","DOIUrl":"10.1007/s00407-023-00311-3","url":null,"abstract":"<div><p>In this paper we publish three fragments of a cuneiform tablet that, when complete, contained the dates and zodiacal positions of Saturn’s synodic phenomena for roughly 60 years. The text is unique in containing comparisons of computed data with observations. Through an analysis of the preserved data we propose that the dates and positions were computed by an otherwise unknown two-zone System A-type scheme and show that the computed data in the tablet can be dated to the fourth century BC. This early date and the comparisons with observations suggest that the text was produced during the period of active development of the planetary systems.</p></div>","PeriodicalId":50982,"journal":{"name":"Archive for History of Exact Sciences","volume":"77 5","pages":"501 - 535"},"PeriodicalIF":0.5,"publicationDate":"2023-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00407-023-00311-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44377583","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}