Archive for History of Exact Sciences最新文献

{"title":"Kepler’s ephemerides of Mars for 1609–1611","authors":"Christián C. Carman","doi":"10.1007/s00407-026-00389-5","DOIUrl":"10.1007/s00407-026-00389-5","url":null,"abstract":"<div><p>Folios 400r–405v of the Pulkovo XIV preserve a set of Martian ephemerides computed by Benjamin Ursinus under Kepler’s direction. They have been read as an incomplete and partly erroneous set of calculations for 1609. This paper shows instead that they form a coherent 3-year sequence, running from 1609 to 1611, whose transitions between years are concealed both by the loss of intermediate sheets and by the fact that the entries are spaced not by the civil calendar but at 10-day intervals from the moment of zero anomaly; the 1611 sequence opens with a fresh determination of the Martian aphelion and a correspondingly new zero of anomaly. A numerical analysis of the 35 surviving entries shows that the solar longitudes were taken from Tycho’s tables reduced to a meridian some 12½ min of time east of Uraniborg, and that the equated anomalies and distances of Mars reproduce, to a few seconds of arc, the values required by the elliptical orbit and the area law with the parameters of the Astronomia Nova. The residual errors of a few arcminutes in heliocentric longitude are traced to the adopted parameters rather than to the model. These sheets are the earliest known ephemerides computed with Kepler’s first two laws.</p></div>","PeriodicalId":50982,"journal":{"name":"Archive for History of Exact Sciences","volume":"80 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2026-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149132451","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":"Roberval optician: a critical edition of De la Dioptrique ou des lunettes with commentary","authors":"Dominique Raynaud","doi":"10.1007/s00407-026-00379-7","DOIUrl":"10.1007/s00407-026-00379-7","url":null,"abstract":"<div><p>This article is devoted to Roberval’s little-known work on optics. After listing the optical manuscripts held in the Archives of the Paris Academy of Sciences, the article provides a critical edition of <i>Livre troisiesme de la Dioptrique ou des lunettes</i> (1648–1651), based on Roberval’s autograph and the copy made by his student François Du Verdus. This fairly long unpublished text (90 pages) is mainly devoted to the study of the anaclastic problem and presents the solutions of the elliptical lens, the hyperbolic lens, and optical eggs, for which Roberval details various geometric constructions.</p></div>","PeriodicalId":50982,"journal":{"name":"Archive for History of Exact Sciences","volume":"80 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2026-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149133352","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":"Paul Hertz’ contribution to proof theory: normal-form results for deductions","authors":"Moritz Bodner","doi":"10.1007/s00407-026-00377-9","DOIUrl":"10.1007/s00407-026-00377-9","url":null,"abstract":"<div><p>Amongst the most central results in proof theory are normal-form results for deductions. Such results were first presented, not by David Hilbert, who first formulated the idea of a mathematical theory of mathematical proofs (in 1904), but by Paul Hertz (in 1922). Hertz’ work (and relationship to Hilbert) has not received the attention it deserves. I discuss both in detail, as well as the theoretical role normal-form results play within proof theory. An unpublished manuscript by Heinrich Behmann commenting on Hertz’ work is published (with translation) as an appendix.</p></div>","PeriodicalId":50982,"journal":{"name":"Archive for History of Exact Sciences","volume":"80 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2026-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13619662/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149082832","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":"Desargues’s last theorem and theory of foci","authors":"Andrea Del Centina","doi":"10.1007/s00407-026-00385-9","DOIUrl":"10.1007/s00407-026-00385-9","url":null,"abstract":"<div><p>In this paper we analyse and comment on the genesis and proof of the theorem that Girard Desargues presented in the last pages of his <i>Brouillon project</i>, and discuss the characterization of the foci of conic sections as fixed points of a certain involution on the principal axis that he tacitly used to establish this theorem.</p></div>","PeriodicalId":50982,"journal":{"name":"Archive for History of Exact Sciences","volume":"80 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2026-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149034630","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 wavelength of light as Thomas Young invented it","authors":"Olivier Morizot","doi":"10.1007/s00407-026-00387-7","DOIUrl":"10.1007/s00407-026-00387-7","url":null,"abstract":"<div><p>This paper documents Thomas Young’s invention of a concept which he alternately refers to as the “magnitude”, “breadth”, “interval”, or “length of an undulation” of light. First, the paper highlights that Young was first to link some concept of a wavelength to a theory of optics and to assign a precise value to this length for each component of the colour spectrum. Then, it sets out an explanation of how Young made up these values, comparing them with the material previously available within Newton’s <i>Opticks</i>. Finally, it examines the reasons why Young introduced an optical wavelength into his theory of light, insofar as these reasons might shed light on why he was first to do so.</p></div>","PeriodicalId":50982,"journal":{"name":"Archive for History of Exact Sciences","volume":"80 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2026-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149034613","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":"Numerical tables in early twentieth-century statistics: accuracy, usage, and computational practices","authors":"Safaa K. Kadhem","doi":"10.1007/s00407-026-00386-8","DOIUrl":"10.1007/s00407-026-00386-8","url":null,"abstract":"<div><p>Before electronic computers, statistical analysis depended on numerical tables that provided discretized approximations to continuous functions. These tables were essential for the biometric and agricultural studies of Karl Pearson and Ronald A. Fisher. Yet, their accuracy has never been systematically examined. This paper compares Pearson’s (1914) and Fisher’s (1925) tables with modern computations. Pearson’s normal tables achieved remarkable accuracy (mean absolute error <span>(4 times 10^{-5})</span>), while errors for the <i>t</i> and Chi-square distributions were larger (up to <span>(5 times 10^{-4})</span>). We examine the computational methods, economic constraints, and contemporary awareness of numerical errors. Discretization errors were small relative to other sources of uncertainty, and the tables were accurate enough for their purposes. This study contributes to the history of statistical computation by providing a quantitative assessment of early twentieth-century table accuracy. The findings reveal the priorities and constraints that shaped table construction, and provide a foundation for understanding the reliability of historical analyses.</p></div>","PeriodicalId":50982,"journal":{"name":"Archive for History of Exact Sciences","volume":"80 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2026-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148927628","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":"Conrad Habicht’s 1914 manuscript on special relativity and Einstein’s 1907 reframing of the 1905 theory","authors":"Hector Giacomini","doi":"10.1007/s00407-026-00384-w","DOIUrl":"10.1007/s00407-026-00384-w","url":null,"abstract":"<div><p>This note examines an apparently unpublished manuscript on special relativity written by Conrad Habicht in 1914 and made available online by the ETH-Bibliothek Zürich in December 2024. To the best of my knowledge, no study of its content has yet been published. Habicht was one of Einstein’s closest companions during the Bern years. Between February 1902 and mid-1904, he shared with Einstein many occasions for discussion and companionship in Bern. After leaving the city, he remained in close contact with Einstein through visits, reciprocal stays, and a substantial correspondence extending from the years immediately following 1905 to the eve of the First World War. The manuscript offers a clear and pedagogical presentation of special relativity. Its historical interest lies in the structure of the exposition and in the memory of the theory that the text preserves. Habicht does not present special relativity as an isolated creation beginning from Einstein’s 1905 paper alone. He devotes considerable space to the pre-Einsteinian problem situation: the classical principle of relativity, the ether, Fizeau’s experiment, Michelson–Morley, Lorentz’s theory, the contraction hypothesis, local time, and the privileged system of the stationary ether. Lorentz is treated as the central figure who brought the electrodynamics of moving bodies to its most acute form before Einstein’s intervention. This note provides a qualitative description of the manuscript, with particular attention to its structure, its treatment of the relation between classical mechanics and electrodynamics, and the respective roles assigned to Lorentz, Michelson–Morley, Einstein, and Minkowski. It also argues that Habicht’s exposition stands much closer to Einstein’s 1907 review article, <i>Über das Relativitätsprinzip und die aus demselben gezogenen Folgerungen</i>, than to the more compressed and self-contained presentation of <i>Zur Elektrodynamik bewegter Körper</i> in 1905. The manuscript thus offers an opportunity to examine a striking shift in Einstein’s own public presentation of special relativity: from the sparse, principle-based narrative of 1905 to the historically reconstructed and Lorentz-centered exposition of 1907. The document is therefore a historically significant witness to the early reception and narration of Einstein’s theory within the circle of one of his closest Bern companions. Its value lies in showing how, within Einstein’s extended milieu, special relativity could be understood not as an isolated act of conceptual creation, but as the principled resolution of a Lorentzian and electrodynamical problem situation.</p></div>","PeriodicalId":50982,"journal":{"name":"Archive for History of Exact Sciences","volume":"80 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2026-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148782086","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":"Joseph Fourier’s courses of analysis at the Ecole Polytechnique (1795–1798): based on a study of two unpublished manuscripts","authors":"Xiaofei Wang","doi":"10.1007/s00407-026-00378-8","DOIUrl":"10.1007/s00407-026-00378-8","url":null,"abstract":"<div><p>The lecture courses given by Augustin–Louis Cauchy, published in 1820 s, contributed decisively to the reputation of the <i>cours d’analyse</i> at the Ecole Polytechnique in history. However, as B. Belhoste has pointed out, the teaching of analysis during the initial 5 year period (1794–1799) of the school was pivotal for the development of analysis in the nineteenth century. Joseph Fourier taught analysis from 1795 to 1798 at this institution, a period that coincided with the delivery of lectures on a more advanced level by Joseph–Louis Lagrange on the same mathematical topic from 1795 to 1799. However, the courses taught by Fourier have been overlooked, either because they were not published as the courses by Lagrange and Cauchy at the Ecole Polytechnique were, or because they were considered to be of lesser importance, being viewed merely as sources for teaching. This paper presents a comprehensive analysis of the two unpublished manuscripts that document Fourier’s pedagogical contributions at the Ecole Polytechnique. These manuscripts, Ms. 1852 and Ms. 2044, offer a unique insight into Fourier’s approach to teaching analysis at the Ecole Polytechnique. Each manuscript comprises notes taken during or produced after the courses taught by Fourier in a specific period, which will be elucidated in a greater detail in the article. The manuscripts are studied as material objects in order to gain insight into the content and textual forms of the documents, which in turn shed light on the teaching and learning activities of analysis at the end of the eighteenth century. The study of these manuscripts highlights that the lecture notes, produced and preserved in manuscript form, offer a unique perspective that published textbooks do not provide. By examining and comparing the manuscripts, this paper establishes that Fourier in fact presented the differential calculus twice to two different classes of students and it also highlights the evolution from one to the other. Furthermore, I argue that Fourier’s pedagogical approach was instrumental in shaping his methodology of the differential calculus. In addition, I bring to light Fourier’s epistemological concerns in dealing with this subject. In his methodology of analysis, Fourier shared with Lagrange an affinity for epistemological values, including simplicity, clarity and rigour. In conclusion, I suggest that an epistemological/mathematical culture took shape in this context, which cannot be dissociated from the enterprise of rigorizing analysis undertaken by Lagrange, then Fourier and subsequently Cauchy at the Ecole Polytechnique.</p></div>","PeriodicalId":50982,"journal":{"name":"Archive for History of Exact Sciences","volume":"80 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2026-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148751535","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 area of a segment in cuneiform mathematics","authors":"Daniel F. Mansfield","doi":"10.1007/s00407-026-00372-0","DOIUrl":"10.1007/s00407-026-00372-0","url":null,"abstract":"<div><p>Archimedes’ treatise <i>Measurement of a Circle</i> is considered the oldest known text concerning circular sectors. We show that the areas of circular sectors and segments were calculated more than a thousand years earlier in ancient Mesopotamia.</p></div>","PeriodicalId":50982,"journal":{"name":"Archive for History of Exact Sciences","volume":"80 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2026-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00407-026-00372-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148750859","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":"Spica and the ancient astronomers: on Hipparchus’s longitude of Spica and the date of Timocharis’s lunar eclipse","authors":"James Evans","doi":"10.1007/s00407-026-00383-x","DOIUrl":"10.1007/s00407-026-00383-x","url":null,"abstract":"<div><p>Hipparchus based an estimate of the minimum possible value for the rate of precession on measurements of the distance of Spica from the Moon in mid-eclipse—an eclipse observed by himself on April 21, 146 BCE and another observed by Timocharis, on an unspecified date. This paper reaches three conclusions: (1) Hipparchus’s final adopted value for the longitude of Spica was determined by his wish to keep the latitude of Spica constant at 2° South; (2) Hipparchus carefully selected two eclipses for comparison so that the effects of the lunar parallax would nearly cancel out; and (3) Timocharis’s lunar eclipse was one of two possibilities: the eclipse of April 19, 295 BCE or that of April 8, 294 BCE.</p></div>","PeriodicalId":50982,"journal":{"name":"Archive for History of Exact Sciences","volume":"80 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2026-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148750526","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}