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Decimal fractional numeration and the decimal point in 15th-century Italy Historia Mathematica (IF 0.5) Pub Date : 2024-02-17 Glen Van Brummelen
The earliest known appearance of the decimal point was in the interpolation column of a sine table in Christopher Clavius's (1593). But this is a curious place to introduce such a significant new idea, and the fact that Clavius never took advantage of it in his own later writings has remained unexplained. We trace Clavius's use of decimal fractional numeration and the decimal point back to the work
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“On the Unviability of Interpreting Leibniz's Infinitesimals through Non-standard analysis” Historia Mathematica (IF 0.5) Pub Date : 2024-01-29 Richard Arthur, David Rabouin
Non-standard analysis has often been presented as the proper framework for expressing rigorously Leibniz's conception of infinitesimals. This paper intends to study this interpretation from an historical point of view and to dispel a series of misunderstandings on which it rests. In order to do so, we propose to go back to Leibniz's conception of quantity, number and magnitude, an approach which has
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Reactionary Mathematics: a Genealogy of Purity, Massimo Mazzotti, University of Chicago Press (2023) Historia Mathematica (IF 0.5) Pub Date : 2023-12-27 Davide Crippa
Abstract not available
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Johannes Regiomontanus, Aufgaben und Übungen zur Algebrass, Jens Høyrup, Martin Hellmann, Erwin Rauner Verlag, Augsburg (2023), Essay review byed., trans Historia Mathematica (IF 0.5) Pub Date : 2023-12-08 Jens Høyrup
Abstract not available
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Review of Jesper Lützen: A History of Mathematical Impossibility, Oxford University Press (2022) Historia Mathematica (IF 0.5) Pub Date : 2023-11-24 Nicolas Michel
Abstract not available
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Newton on constructions in geometry Historia Mathematica (IF 0.5) Pub Date : 2023-11-10 Viktor Blåsjö
Newton was critical of Descartes's constructivist vision of the foundations of geometry organised around certain curve-tracing principles. In unpublished work, Newton outlined a constructivist program of his own, based on his “organic” method of curve tracing, which subsumes Descartes's emblematic turning-ruler-and-moving-curve construction method as a special case, but does not suffer from the latter's
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A determination of Catalan numbers in 18th century Italy by Giovanni Rizzetti (1675–1751) Historia Mathematica (IF 0.5) Pub Date : 2023-10-09 Alessandro Belcastro, Giuseppina Fenaroli
We discuss the probabilistic question faced by the Italian scholar Giovanni Rizzetti (1675–1751) and suggest this is a variant of what we refer to today as the “ballot sequences”, variant to which Catalan numbers offer a solution. Rizzetti's search for a solution led him to produce an iterative rule which involved the consideration of Catalan numbers. Although coming up with these were not his final
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Cyclic quadrilaterals: Solutions of two Japanese problems and their proofs Historia Mathematica (IF 0.5) Pub Date : 2023-10-02 J. Marshall Unger
Late 18th and early 19th century Japanese mathematicians (wasanka) found solutions of two problems concerning the incircles of the quarter-triangles and skewed sectors of cyclic quadrilaterals. There is a modern proof of the first solution, but it makes extensive use of trigonometry and is therefore unlikely to be what a wasanka would have written. As for the second solution, Aida Yasuaki (1747–1817)
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A New History of Greek Mathematics, Reviel Netz, Cambridge University Press, Cambridge (2022) Historia Mathematica (IF 0.5) Pub Date : 2023-09-22 Michalis Sialaros
Abstract not available
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Abstracts Historia Mathematica (IF 0.5) Pub Date : 2023-08-14 Duncan J. Melville, Kim Plofker
Abstract not available
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Adam Ries, Coß 1. 2 vols., Bernd Rüdiger, Gebhardt Rainer, Menso Folkerts (Eds.), Adam-Ries-Bund, Annaberg-Buchholz (2023), 320+278 pp.1 Historia Mathematica (IF 0.5) Pub Date : 2023-08-03 Jens Høyrup
Abstract not available
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Da Vinci's Codex Atlanticus, fols. 395r and 686r–686v, refers to Leonardo Pisano volgarizzato, not to Giorgio Valla Historia Mathematica (IF 0.5) Pub Date : 2023-07-11 Dominique Raynaud
This article aims at identifying the sources of fols. 395r and 686r-686v of the Codex Atlanticus. These anonymous folios, inserted in Leonardo da Vinci's notebooks, do not deal with the duplication of the cube proper, nor do they derive from Giorgio Valla's De expetendis et fugiendis rebus (1501), as has been claimed. They deal specifically with the extraction of the cube root by geometric methods
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Julius Plücker – A path from geometry to optics Historia Mathematica (IF 0.5) Pub Date : 2023-07-06 Michael Wiescher
This paper evaluates possible reasons and motivations for 19th century geometer Julius Plücker's change in direction from his purely mathematical work to experimental physics. The author argues that this change did not happen suddenly in 1846 as is frequently suggested but rather, was a gradual change. This move took more than a decade and was triggered by Plücker's idea to apply his mathematical formalism
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Scientia Perspectiva. Leibniz and geometric perspective Historia Mathematica (IF 0.5) Pub Date : 2023-06-16 Valérie Debuiche, Mattia Brancato
Leibniz's manuscripts on perspective geometry remained unpublished and unknown until very recently. Among them, Scientia perspectiva stands out as the most complex and the most original. In this paper, we offer a thorough analysis of this manuscript, showing how Leibniz moves from perspective concepts fairly common at that time to a completely new idea of the practice that could have affected its entire
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Felix Klein's teaching of Galois theory Historia Mathematica (IF 0.5) Pub Date : 2023-06-14 Henning Heller
This article concerns a lecture course on Galois theory held by Felix Klein in summer 1886 at the University of Göttingen. Klein's commitment to teaching the theory of equations from Galois's advanced point of view forms a remarkable exception within the European curriculum. Klein's heuristic methodology, in which mathematical theory is extracted from a gradually advancing set of examples, allowed
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Abstracts Historia Mathematica (IF 0.5) Pub Date : 2023-05-19 Duncan J. Melville, Kim Plofker
Abstract not available
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Abstracts Historia Mathematica (IF 0.5) Pub Date : 2023-04-27 Duncan J. Melville, Kim Plofker
Abstract not available
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„Kann eine Frau Privatdozentin werden?“ - die Umfrage des Preußischen Kultusministeriums zur Habilitation von Frauen 1907, Cordula Tollmien, tredition, Hamburg (2021), 296 S., 19,99 €, ISBN: 978-3-347-05156-0 Historia Mathematica (IF 0.5) Pub Date : 2023-04-20 David E. Rowe
Abstract not available
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Editorial Historia Mathematica (IF 0.5) Pub Date : 2023-02-28 Antoni Malet, Jeffrey Oaks
Abstract not available
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Abstracts Historia Mathematica (IF 0.5) Pub Date : 2023-02-08 Duncan J. Melville, Kim Plofker
Abstract not available
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Pygmies, Bushmen, and savage numbers – a case study in a sequence of bad citations Historia Mathematica (IF 0.5) Pub Date : 2023-01-11 Antti J.V. Tuominen
There is a prevalent claim in the literature examining the history of numbers and the development of number words that some African group (“Bushmen” or “Pygmies”) counts in a particular way, where their numerals are of the form 1, 2, 3, 2+2, 2+2+1, etc. Numerous forms of this claim are traced back to their original sources through an extensive search of the available literature. The author argues that
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Poncelet's discovery of homology Historia Mathematica (IF 0.5) Pub Date : 2023-01-06 Christopher Baltus
Homology was among the concepts introduced in Jean Victor Poncelet's 1822 Traité des Propriétés Projectives des Figures. Homology is a projective transformation which has an axis, a line of fixed points. The Traité develops a straightedge construction of points under homology, essentially that found in work on perspective drawing and by Phillipe de la Hire, 1673. However, Poncelet's very distinct path
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“Perfect Arithmetic” by Vaclav Josef Pelikan Historia Mathematica (IF 0.5) Pub Date : 2023-01-06 Dmitry Zlatopolski
The present article describes for the first time the book of Vaclav Josef Pelikan titled Arithmeticus Perfectus Qui tria numerare nescit. Seu Arithmetica dualis, In qua Numerando non proceditur, nisi ad duo, & tamen omnes quaestiones Arithmeticae negotio facili enodari possunt, published in Prague in 1712. The book is written in Latin on 86 pages and consists of a dedication, a message to the reader
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On five sangaku problems appearing in Yamaguchi's travel diary Historia Mathematica (IF 0.5) Pub Date : 2022-11-14 David Clark, Todd Munson
Abstract not available
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How Leibniz tried to tell the world he had squared the circle Historia Mathematica (IF 0.5) Pub Date : 2022-11-09 Lloyd Strickland
In 1682, Leibniz published an essay containing his solution to the classic problem of squaring the circle: the alternating converging series that now bears his name. Yet his attempts to disseminate his quadrature results began seven years earlier and included four distinct approaches: the conventional (journal article), the grand (treatise), the impostrous (pseudepigraphia), and the extravagant (medals)
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Felice Casorati and the reception of Gaussian optics in Italy Historia Mathematica (IF 0.5) Pub Date : 2022-11-09 Arrigo Pisati, Riccardo Rosso
We analyze the work on geometrical optics by Felice Casorati who contributed to the dissemination of Gaussian optics in Italy. In his approach to Gauss's (1840) Untersuchungen he applied determinants to describe multiple refractions in an optical system and he explored the extension of the theory to cover slightly non-centered optical systems for which he introduced the cardinal line, a straight line
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Abstracts Historia Mathematica (IF 0.5) Pub Date : 2022-11-08 Duncan J. Melville, Kim Plofker
Abstract not available
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The origins of the fundamental theorem of surface theory Historia Mathematica (IF 0.5) Pub Date : 2022-11-07 Alberto Cogliati, Rachele Rivis
The Mainardi-Codazzi equations (MCE) and the fundamental theorem of surface theory (FT) are regarded as crucial achievements in the development of surface theory. The paper offers an analysis of three papers by Bour, Codazzi and Bonnet, submitted on the occasion of the Grand Prix des Mathématiques (1859), in which the MCE and the FT were systematically employed to deal with applicability problems.
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How the estimate of 2 on YBC 7289 may have been calculated Historia Mathematica (IF 0.5) Pub Date : 2022-10-21 David Buckle
It remains unknown how the approximation of 2 scribed on Babylonian tablet YBC 7289 was calculated. In this article I show how it can be straightforwardly computed using a well-known regular number as the input for the Babylonian method of estimating square roots. My objective is to demonstrate that Babylonian mathematics was sufficiently evolved for the approximation to be easily derived and thus
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Abstracts Historia Mathematica (IF 0.5) Pub Date : 2022-08-26 Duncan J. Melville, Kim Plofker
Abstract not available
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Felix Hausdorff's Collected Works – a meta-review Historia Mathematica (IF 0.5) Pub Date : 2022-08-19 Reinhard Siegmund-Schultze
Abstract not available
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Federigo Enriques (1871-1946): A critical study of Lezioni di geometria proiettiva Historia Mathematica (IF 0.5) Pub Date : 2022-08-17 M.G. Lugaresi, C. D'Alterio
Federigo Enriques (1871-1946) was a protagonist of mathematical culture in the early twentieth century. The handbook prepared for one of his university courses at the University of Bologna, Lezioni di geometria proiettiva, constitutes probably the most representative work of his early teaching years. This book has influenced several Enriques' researches, and in particular those relating to the foundations
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Ajima's solution to the Gion shrine problem: A modern interpretation Historia Mathematica (IF 0.5) Pub Date : 2022-08-10 Hidetoshi Fukagawa, David Clark
This geometry problem rose to great prominence among Japan's mathematicians after it was posted on a sangaku in 1749. Several scholars presented solutions, most famously Ajima Naonobu in 1774. Here we present Ajima's celebrated solution, along with a modern interpretation of his analysis, which notably employs the computation of a determinant via cofactor expansion. This article consists, in large
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On a sangaku of Sugino'o Shrine (Yamagata) and Yamaguchi Kanzan's second trip Historia Mathematica (IF 0.5) Pub Date : 2022-08-05 Peter Wong
In the preamble of the 1818 sangaku tablet of Sugino'o Shrine, the proposers acknowledged the help of an unnamed teacher/master in understanding and solving certain mathematical problems. Endō Tadashi argued that this unnamed teacher could be Saitō Naonaka (1773-1844). In this paper, we examine the famous travel diary of Yamaguchi Kanzan (?-1850) especially on his second trip to the Northeast. We compare
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Mathematics and philology: An example from wasan Historia Mathematica (IF 0.5) Pub Date : 2022-06-09 J. Marshall Unger
Fukagawa and Rothman introduced a difficult wasan problem concerning an ellipse inscribed in a right triangle from an old travel diary. Like the famous Gion Shrine problem, it does not specify numerical data but asks only for an equation of a particular kind; moreover, modern solutions of the problem entail polynomial equations of degree greater than four. One may therefore wonder whether the problem
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Introduction – A critical approach to the opposition between “concrete” and “abstract” numbers Historia Mathematica (IF 0.5) Pub Date : 2022-06-02 Christine Proust, Eric Vandendriessche
Abstract not available
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The sexagesimal place-value notation and abstract numbers in mathematical cuneiform texts Historia Mathematica (IF 0.5) Pub Date : 2022-04-07 Christine Proust
The discovery at the end of the 19th century of the mathematical cuneiform texts posed to historians the question of the nature of the numbers used in them, i.e. that of the sexagesimal place-value notation. This notation, although familiar to us today since it is the one we use to measure time, has, in the cuneiform texts, specificities which still raise challenges of interpretation. One of these
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The concrete numbers of “primitive” societies: A historiographical approach Historia Mathematica (IF 0.5) Pub Date : 2022-03-28 Eric Vandendriessche
From the 19th century onwards, some mathematicians and philosophers (G. Peacock, L. Conant, L. Lévy-Bruhl, L. Brunschvicg et al.), analyzed the numerical systems in use in so-called primitive societies as having a more “concrete” (or less “abstract”) character than those developed in more “advanced” societies. This article aims to better understand—and compare—what this opposition between “abstract
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Modern light on ancient feud: Robert Hooke and Newton's graphical method Historia Mathematica (IF 0.5) Pub Date : 2022-03-10 Siu A. Chin
The feud between Robert Hooke and Isaac Newton, over whether Newton should have acknowledged Hooke's influence on his graphical method of constructing planet orbits, the celebrated Proposition 1, Theorem 1 of the Principia, has remained ongoing among their respective supporters, even after 300 years. The drama has escalated in recent decades, with a claim that Hooke may have used the same method and
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In memoriam: Richard P. Lorch (1942–2021) Historia Mathematica (IF 0.5) Pub Date : 2022-02-01 Henry Zepeda,Benno van Dalen,Menso Folkerts
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From lattices via social history to theories of modernity in mathematics Historia Mathematica (IF 0.5) Pub Date : 2022-02-01 Reinhard Siegmund-Schultze
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Abstracts Historia Mathematica (IF 0.5) Pub Date : 2022-01-31 Duncan J. Melville, Kim Plofker
Abstract not available
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“Denominate numbers” in mathematics school textbooks by Stefan Banach Historia Mathematica (IF 0.5) Pub Date : 2021-12-09 Karolina Karpińska
The paper is dedicated to analysing the role of “denominate numbers” in textbooks for Polish schools, whose author or co-author was Stefan Banach. Banach used the concepts of “number” and “denominate number” in his textbooks. The ways of introducing these concepts, as well as the associated manner of understanding numeration, are analysed in the paper. The methods of manipulating “denominate numbers”
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François Viète's method for calculating the eccentricity in a bisected model and its possible application to Kepler's Vicarious Hypothesis Historia Mathematica (IF 0.5) Pub Date : 2021-12-08 Christián C. Carman
According to Kepler's own words in Astronomia Nova, he invested five years trying to find the values for the eccentricities for his “vicarious” hypothesis. At some point, he asked Herwart von Hohenburg, to ask François Viète's help to solve his problem, but there is no evidence that Viète received this request. At that time, Viète was working on his unpublished Ad harmonicon coeleste. In it, he proposes
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The 1804 examination for the chair of Elementary Mathematics at the University of Prague Historia Mathematica (IF 0.5) Pub Date : 2021-10-13 Elías Fuentes Guillén, Davide Crippa
In 1804 the chair of Elementary Mathematics at Prague University became vacant and a selection procedure, which consisted of a written and an oral examination, was announced. Only Bernard Bolzano and Ladislav Jandera took part in it. Jandera was appointed to the chair, whereas Bolzano became Professor of “Religious Doctrine.” In this paper we examine the context of this Concursprüfung, the performance