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The six books of Diophantus’ Arithmetic increased and reduced to specious: the lost manuscript of Jacques Ozanam (1640–1718) Archive for History of Exact Sciences (IF 0.559) Pub Date : 2021-04-13 Francisco Gómez-García, Pedro J. Herrero-Piñeyro, Antonio Linero-Bas, Ma. Rosa Massa-Esteve, Antonio Mellado-Romero
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
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A study of Babylonian records of planetary stations Archive for History of Exact Sciences Pub Date : 2021-02-18 J. M. Steele, E. L. Meszaros
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
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Einstein on involutions in projective geometry Archive for History of Exact Sciences Pub Date : 2021-01-08 Tilman Sauer, Tobias Schütz
We discuss Einstein’s knowledge of projective geometry. We show that two pages of Einstein’s Scratch Notebook from around 1912 with geometrical sketches can directly be associated with similar sketches in manuscript pages dating from his Princeton years. By this correspondence, we show that the sketches are all related to a common theme, the discussion of involution in a projective geometry setting
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A study of Babylonian planetary theory III. The planet Mercury Archive for History of Exact Sciences Pub Date : 2021-01-03 Teije de Jong
In this series of papers I attempt to provide an answer to the question how the Babylonian scholars arrived at their mathematical theory of planetary motion. Papers I and II were devoted to system A theory of the outer planets and of the planet Venus. In this third and last paper I will study system A theory of the planet Mercury. Our knowledge of the Babylonian theory of Mercury is at present based
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The gravitational influence of Jupiter on the Ptolemaic value for the eccentricity of Saturn Archive for History of Exact Sciences Pub Date : 2021-01-03 Christián C. Carman
The gravitational influence of Jupiter on Saturn produces, among other things, non-negligible changes in the eccentricity of Saturn that affect the magnitude of error of Ptolemaic astronomy. The value that Ptolemy obtained for the eccentricity of Saturn is a good approximation of the real eccentricity—including the perturbation of Jupiter—that Saturn had during the time of Ptolemy's planetary observations
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The development of the concept of uniform convergence in Karl Weierstrass’s lectures and publications between 1861 and 1886 Archive for History of Exact Sciences Pub Date : 2020-12-23 Klaus Viertel
The history of uniform convergence is typically focused on the contributions of Cauchy, Seidel, Stokes, and Björling. While the mathematical contributions of these individuals to the concept of uniform convergence have been much discussed, Weierstrass is considered to be the actual inventor of today’s concept. This view is often based on his well-known article from 1841. However, Weierstrass’s works
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BM 76829: A small astronomical fragment with important implications for the Late Babylonian Astronomy and the Astronomical Book of Enoch Archive for History of Exact Sciences Pub Date : 2020-12-21 Jeanette C. Fincke, Wayne Horowitz, Eshbal Ratzon
BM 76829, a fragment from the mid-section of a small tablet from Sippar in Late Babylonian script, preserves what remains of two new unparalleled pieces from the cuneiform astronomical repertoire relating to the zodiac. The text on the obverse assigns numerical values to sectors assigned to zodiacal signs, while the text on the reverse seems to relate zodiacal signs with specific days or intervals
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Back to the roots of vector and tensor calculus: Heaviside versus Gibbs Archive for History of Exact Sciences Pub Date : 2020-11-10 Alessio Rocci
In June 1888, Oliver Heaviside received by mail an officially unpublished pamphlet, which was written and printed by the American author Willard J. Gibbs around 1881–1884. This original document is preserved in the Dibner Library of the History of Science and Technology at the Smithsonian Institute in Washington DC. Heaviside studied Gibbs’s work very carefully and wrote some annotations in the margins
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Correction to: What Heinrich Hertz discovered about electric waves in 1887–1888 Archive for History of Exact Sciences Pub Date : 2020-11-03 Jed Buchwald, Chen-Pang Yeang, Noah Stemeroff, Jenifer Barton, Quinn Harrington
Unfortunately, only after online first article publication, it was noticed that the first four sentences in footnote two were incorrect.
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Hobbes’s model of refraction and derivation of the sine law Archive for History of Exact Sciences Pub Date : 2020-11-02 Hao Dong
This paper aims both to tackle the technical issue of deciphering Hobbes’s derivation of the sine law of refraction and to throw some light to the broader issue of Hobbes’s mechanical philosophy. I start by recapitulating the polemics between Hobbes and Descartes concerning Descartes’ optics. I argue that, first, Hobbes’s criticisms do expose certain shortcomings of Descartes’ optics which presupposes
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Operator calculus: the lost formulation of quantum mechanics Archive for History of Exact Sciences (IF 0.559) Pub Date : 2020-10-07 Gonzalo Gimeno, Mercedes Xipell, Marià Baig
Traditionally, “the operator calculus of Born and Wiener” has been considered one of the four formulations of quantum mechanics that existed in 1926. The present paper reviews the operator calculus as applied by Max Born and Norbert Wiener during the last months of 1925 and the early months of 1926 and its connections with the rise of the new quantum theory. Despite the relevance of this operator calculus
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Pipe flow: a gateway to turbulence Archive for History of Exact Sciences (IF 0.559) Pub Date : 2020-10-02 Michael Eckert
Pipe flow has been a challenge that gave rise to investigations on turbulence—long before turbulence was discerned as a research problem in its own right. The discharge of water from elevated reservoirs through long conduits such as for the fountains at Versailles suggested investigations about the resistance in relation to the different diameters and lengths of the pipes as well as the speed of flow
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What Heinrich Hertz discovered about electric waves in 1887–1888 Archive for History of Exact Sciences Pub Date : 2020-09-25 Jed Buchwald, Chen-Pang Yeang, Noah Stemeroff, Jenifer Barton, Quinn Harrington
Among the most influential and well-known experiments of the 19th century was the generation and detection of electromagnetic radiation by Heinrich Hertz in 1887–1888, work that bears favorable comparison for experimental ingenuity and influence with that by Michael Faraday in the 1830s and 1840s. In what follows, we pursue issues raised by what Hertz did in his experimental space to produce and to
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Before the end of an error: Giovanni Bianchini’s original flawed treatise on the conversion of stellar coordinates Archive for History of Exact Sciences Pub Date : 2020-09-24 Glen Van Brummelen
In my 2018 article in this journal, I described 15th-century Italian astronomer Giovanni Bianchini’s treatment of the problem of stellar coordinate conversion in his Tabulae primi mobilis, the first correct European solution. In this treatise Bianchini refers to a book he had written previously, containing the same error that had plagued his predecessors’ work on the problem. In this article, we announce
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Impact of Gibbs’ and Duhem’s approaches to thermodynamics on the development of chemical thermodynamics Archive for History of Exact Sciences Pub Date : 2020-09-02 Photis Dais
From 1873 to 1878, the American physicist Josiah Willard Gibbs offered to the scientific community three great articles that proved to be a milestone for the science of thermodynamics. On the other hand, between 1886 and 1896, the French physicist Pierre Maurice Marie Duhem translated thermodynamics into the language of Lagrange’s analytical mechanics. At the same time, he expanded its scope to include
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An unpublished manuscript of John von Neumann on shock waves in boostered detonations: historical context and mathematical analysis Archive for History of Exact Sciences Pub Date : 2020-08-18 Molly Riley Knoedler, Julianna C. Kostas, Caroline Mary Hogan, Harper Kerkhoff, Chad M. Topaz
We report on an unpublished and previously unknown manuscript of John von Neumann and contextualize it within the development of the theory of shock waves and detonations during the nineteenth and twentieth centuries. Von Neumann studies bombs comprising a primary explosive charge along with explosive booster material. His goal is to calculate the minimal amount of booster needed to create a sustainable
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Maurice Janet’s algorithms on systems of linear partial differential equations Archive for History of Exact Sciences Pub Date : 2020-08-10 Kenji Iohara, Philippe Malbos
This article describes the emergence of formal methods in theory of partial differential equations (PDE) in the French school of mathematics through Janet’s work in the period 1913–1930. In his thesis and in a series of articles published during this period, Janet introduced an original formal approach to deal with the solvability of the problem of initial conditions for finite linear PDE systems.
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Babylonian astronomy: a new understanding of column Φ Archive for History of Exact Sciences Pub Date : 2020-08-06 Lis Brack-Bernsen
The most discussed and mysterious column within the Babylonian astronomy is column Φ. It is closely connected to the lunar velocity and to the duration of the Saros. This paper presents new ideas for the development and interpretation of column Φ. It combines the excellent Goal-Year method (for the prediction of Lunar Six time intervals) with old ideas and practices from the “schematic astronomy”.
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On the making of Ptolemy’s star catalog Archive for History of Exact Sciences Pub Date : 2020-08-05 Christian Marx
The assumption that Ptolemy adopted star coordinates from a star catalog by Hipparchus is investigated based on Hipparchus’ equatorial star coordinates in his Commentary on the phenomena of Aratus and Eudoxus. Since Hipparchus’ catalog was presumably based on an equatorial coordinate system, his star positions must have been converted into the ecliptical system of Ptolemy’s catalog in his Almagest
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Tycho Brahe’s Calculi ad Corrigenda Elementa Orbitae Saturni and the technical aspects of his planetary model of Saturn Archive for History of Exact Sciences Pub Date : 2020-08-04 Christián C. Carman
Tycho Brahe was not just an observer; he was a skilled theoretical astronomer, as his lunar and solar models show. Still, even if he is recognized for proposing the Geoheliocentric system, little do we know of the technical details of his planetary models, probably because he died before publishing the last two volumes of his Astronomiae Instaurandae Progymnasmata, which he planned to devote to the
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Babylonian observations of a unique planetary configuration Archive for History of Exact Sciences Pub Date : 2020-08-03 Teije de Jong, Hermann Hunger
In this paper, we discuss Babylonian observations of a “massing of the planets” reported in two Astronomical Diaries, BM 32562 and BM 46051. This extremely rare astronomical phenomenon was observed in Babylon between 20 and 30 March 185 BC shortly before sunrise when all five planets were simultaneously visible for about 10 to 15 min close to the horizon in the eastern morning sky. These two observational
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On Peirce’s 1878 article ‘ The probability of induction ’: a conceptualistic appraisal Archive for History of Exact Sciences Pub Date : 2020-07-28 G. A. Kyriazis
Charles Sanders Peirce wrote the article ‘The probability of induction’ in 1878. It was the fourth article of the series ‘Illustrations of the Logic of Science’ which comprised a total of six articles. According to Peirce, to get a clear idea of the conception of probability, one has ‘to consider what real and sensible difference there is between one degree of probability and another.’ He endorsed
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Pascal’s mystic hexagram, and a conjectural restoration of his lost treatise on conic sections Archive for History of Exact Sciences Pub Date : 2020-07-08 Andrea Del Centina
Through an in-depth analysis of the notes that Leibniz made while reading Pascal’s manuscript treatise on conic sections, we aim to show the real extension of what he called “hexagrammum mysticum”, and to highlight the main results he achieved in this field, as well as proposing plausible proofs of them according to the methods he seems to have developed.
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Polygons of Petrović and Fine, algebraic ODEs, and contemporary mathematics Archive for History of Exact Sciences Pub Date : 2020-06-29 Vladimir Dragović, Irina Goryuchkina
In this paper, we study the genesis and evolution of geometric ideas and techniques in investigations of movable singularities of algebraic ordinary differential equations. This leads us to the work of Mihailo Petrović on algebraic differential equations (ODEs) and in particular the geometric ideas expressed in his polygon method from the final years of the nineteenth century, which have been left
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Mathématiques et architecture: le tracé de l’entasis par Nicolas-François Blondel Archive for History of Exact Sciences Pub Date : 2020-04-23 Dominique Raynaud
In Resolution des quatre principaux problemes d’architecture (1673) then in Cours d’architecture (1683), the architect–mathematician Nicolas-Francois Blondel addresses one of the most famous architectural problems of all times, that of the reduction in columns (entasis). The interest of the text lies in the variety of subjects that are linked to this issue. (1) The text is a response to the challenge
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Poincaré’s stated motivations for topology Archive for History of Exact Sciences Pub Date : 2020-03-04 Lizhen Ji, Chang Wang
It is well known that one of Poincaré’s most important contributions to mathematics is the creation of algebraic topology. In this paper, we examine carefully the stated motivations of Poincaré and potential applications he had in mind for developing topology. Besides being an interesting historical problem, this study will also shed some light on the broad interest of Poincaré in mathematics in a
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Borelli’s edition of books V–VII of Apollonius’s Conics, and Lemma 12 in Newton’s Principia Archive for History of Exact Sciences Pub Date : 2020-01-10 Andrea Del Centina, Alessandra Fiocca
To solve the direct problem of central forces when the trajectory is an ellipse and the force is directed to its centre, Newton made use of the famous Lemma 12 (Principia, I, sect. II) that was later recognized equivalent to proposition 31 of book VII of Apollonius’s Conics. In this paper, in which we look for Newton’s possible sources for Lemma 12, we compare Apollonius’s original proof, as edited
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A proto-Normal Star Almanac dating to the reign of Artaxerxes III: BM 65156 Archive for History of Exact Sciences Pub Date : 2020-01-02 John Steele
Babylonian methods for predicting planetary phenomena using the so-called goal-year periods are well known. Texts known as Goal-Year Texts contain collections of the observational data needed to make predictions for a given year. The predictions were then recorded in Normal Star Almanacs and Almanacs. Large numbers of Goal-Year Texts, Normal Star Almanacs and Almanacs are attested from the early third
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The Principia’s second law (as Newton understood it) from Galileo to Laplace Archive for History of Exact Sciences Pub Date : 2019-11-26 Bruce Pourciau
Newton certainly regarded his second law of motion in the Principia as a fundamental axiom of mechanics. Yet the works that came after the Principia, the major treatises on the foundations of mechanics in the eighteenth century—by Varignon, Hermann, Euler, Maclaurin, d’Alembert, Euler (again), Lagrange, and Laplace—do not record, cite, discuss, or even mention the Principia’s statement of the second
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The Jalālī Calendar: the enigma of its radix date Archive for History of Exact Sciences Pub Date : 2019-11-12 Hamid-Reza Giahi Yazdi
The Jalālī (or Malikī) Calendar is well known to Iranian and Western researchers. It was established by the order of Sulṭān Jalāl al-Dīn Malikshāh-i Saljūqī in the 5th c. A.H. (The dates which are designated with A.H. indicate the Hijrī Calendar.)/11th c. A.D. in Isfahan. After the death of Yazdigird III (the last king of the Sassanid dynasty), the Yazdigirdī Calendar, as a solar one, gradually lost
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Une controverse entre Émile Picard et Leopold Kronecker Archive for History of Exact Sciences Pub Date : 2019-11-09 Cédric Vergnerie
Dans deux articles publiés en 1869 et 1878, Leopold Kronecker construit une théorie qui prend sa source dans le travail de Sturm sur la détermination du nombre de solutions réelles d’une équation. La présentation de cette théorie des caractéristiques par Émile Picard va donner lieu à une controverse entre les deux mathématiciens sur la paternité d’une formule donnant le nombre de solutions de certains
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What were the genuine Banach spaces in 1922? Reflection on axiomatisation and progression of the mathematical thought Archive for History of Exact Sciences Pub Date : 2019-10-26 Frédéric Jaëck
This paper provides an analysis of the use of axioms in Banach’s Ph.D. and their role in the progression of Banach’s mathematical thought. In order to give a precise account of the role of Banach’s axioms, we distinguish two levels of activity. The first one is devoted to the overall process of creating a new theory able to answer some prescribed problems in functional analysis. The second one concentrates
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How to notate a crossing of strings? On Modesto Dedò’s notation of braids Archive for History of Exact Sciences Pub Date : 2019-10-10 Michael Friedman
As is well known, it was only in 1926 that a comprehensive mathematical theory of braids was published—that of Emil Artin. That said, braids had been researched mathematically before Artin’s treatment: Alexandre Theophile Vandermonde, Carl Friedrich Gauß and Peter Guthrie Tait had all attempted to introduce notations for braids. Nevertheless, it was only Artin’s approach that proved to be successful
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Babylonian solar theory on the Antikythera mechanism Archive for History of Exact Sciences Pub Date : 2019-09-20 James Evans, Christián C. Carman
This article analyzes the angular spacing of the degree marks on the zodiac scale of the Antikythera mechanism and demonstrates that over the entire preserved 88° of the zodiac, the marks are systematically placed too close together to be consistent with a uniform distribution over 360°. Thus, in some other part of the zodiac scale (not preserved), the degree marks have been spaced farther apart. By
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The law of refraction and Kepler’s heuristics Archive for History of Exact Sciences Pub Date : 2019-08-31 Carlos Alberto Cardona Suárez, Juliana Gutiérrez Valderrama
Johannes Kepler dedicated much of his work to discover a law for the refraction of light. Unfortunately, he formulated an incorrect law. Nevertheless, it was useful for anticipating the behavior of light in some specific conditions. Some believe that Kepler did not have the elements to formulate the law that was later accepted by the scientific community, that is, the Snell–Descartes law. However,
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Andalò di Negro’s De compositione astrolabii: a critical edition with English translation and notes Archive for History of Exact Sciences Pub Date : 2019-08-22 Dominique Raynaud, Samuel Gessner, Bernardo Mota
In this article, we publish the critical edition of Andalo di Negro’s De compositione astrolabii, with English translation and commentary. The mathematician and astronomer Andalo di Negro (Genoa ca. 1260–Naples 1334) presumably redacted this treatise on the astrolabe in the 1330s, while residing at the court of King Robert of Naples. The present edition has three purposes: first, to make available
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Correction to: The Back Plate Inscription and eclipse scheme of the Antikythera Mechanism revisited Archive for History of Exact Sciences Pub Date : 2019-07-13 Paul Iversen, Alexander Jones
Tables 2 and 4 contained an incorrect set of values for the mean lunar latitudes associated with the tabulated eclipse possibilities.
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Lebesgue’s criticism of Carl Neumann’s method in potential theory Archive for History of Exact Sciences Pub Date : 2019-07-09 Ivan Netuka
In the 1870s, Carl Neumann proposed the so-called method of the arithmetic mean for solving the Dirichlet problem on convex domains. Neumann’s approach was considered at the time to be a reliable existence proof, following Weierstrass’s criticism of the Dirichlet principle. However, in 1937 H. Lebesgue pointed out a serious gap in Neumann’s proof. Curiously, the erroneous argument once again involved
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Ibn al-Fahhād and the Great Conjunction of 1166 AD Archive for History of Exact Sciences Pub Date : 2019-07-08 S. Mohammad Mozaffari
Farīd al-Dīn Abu al-Ḥasan ‘Alī b. al-Fahhād’s astronomical tradition as represented in the prolegomenon to his Alā’ī zīj (1172 AD) shows his experimental examination of the theories of his predecessors and testing the circumstances of the synodic phenomena as derived from the theories developed in the classical period of medieval Middle Eastern astronomy against his own observations. This work was
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On the youthful writings of Louis J. Mordell on the Diophantine equation $$y^2-k=x^3$$ y 2 - k = x 3 Archive for History of Exact Sciences Pub Date : 2019-06-25 Sébastien Gauthier, François Lê
This article examines the research of Louis J. Mordell on the Diophantine equation $$y^2-k=x^3$$ as it appeared in one of his first papers, published in 1914. After presenting a number of elements relating to Mordell’s mathematical youth and his (problematic) writing, we analyze the 1914 paper by following the three approaches he developed therein, respectively, based on the quadratic reciprocity law
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The Back Plate Inscription and eclipse scheme of the Antikythera Mechanism revisited Archive for History of Exact Sciences Pub Date : 2019-06-24 Paul Iversen, Alexander Jones
This paper presents a new edition of the Back Plate Inscription (BPI) of the Antikythera Mechanism, a series of descriptions of circumstances associated with eclipses indicated cyclically by the inscriptions of the Mechanism’s Saros Dial Scale. Our edition features several significant new readings as well as the confirmation of a disputed reading pertaining to one of the index letters by which the
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Deducing Newton’s second law from relativity principles: A forgotten history Archive for History of Exact Sciences Pub Date : 2019-06-13 Olivier Darrigol
In French mechanical treatises of the nineteenth century, Newton’s second law of motion was frequently derived from a relativity principle. The origin of this trend is found in ingenious arguments by Huygens and Laplace, with intermediate contributions by Euler and d’Alembert. The derivations initially relied on Galilean relativity and impulsive forces. After Bélanger’s Cours de mécanique of 1847,
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Thomas Harriot on the coinage of England Archive for History of Exact Sciences Pub Date : 2019-05-20 Norman Biggs
Thomas Harriot was the finest English mathematician before Isaac Newton, but his work on the coinage of his country is almost unknown, unlike Newton’s. In the early 1600s Harriot studied several aspects of the gold and silver coins of his time. He investigated the ratio between the values of gold and silver, using data derived from the official weights of the coins; he used hydrostatic weighing to
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A study of Babylonian planetary theory II. The planet Venus Archive for History of Exact Sciences Pub Date : 2019-03-29 Teije de Jong
AbstractIn this series of papers, I attempt to provide an answer to the question how the Babylonian scholars arrived at their mathematical theory of planetary motion. Paper I (de Jong in Arch Hist Exact Sci 73:1–37, 2019) was devoted to a study of system A theory of the outer planets. In this second paper, I will study system A theory of the planet Venus. All presently known ephemerides of Venus appear
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The medieval Moon in a matrix: double argument tables for lunar motion Archive for History of Exact Sciences Pub Date : 2019-03-29 José Chabás, Bernard R. Goldstein
AbstractAstronomers have always considered the motion of the Moon as highly complicated, and this motion is decisive in determining the circumstances of such critical celestial phenomena as eclipses. Table-makers devoted much ingenuity in trying to find ways to present it in tabular form. In the late Middle Ages, double argument tables provided a smart and compact solution to address this problem satisfactorily
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Jost Bürgi’s methods of calculating sines, and possible transmission from India Archive for History of Exact Sciences Pub Date : 2019-03-14 Roy Wagner, Samuel Hunziker
AbstractA few years ago, a manuscript by Jost Bürgi (1552–1632) was brought to scholarly attention, which included an ingenious sine calculation method. The purpose of this paper is to discuss two aspects of this manuscript. First, we wish to improve the current understanding of Bürgi’s method of sine calculation, especially with respect to the calculation of sines at a resolution of 1 min. Second
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There is no consequentia mirabilis in Greek mathematics Archive for History of Exact Sciences Pub Date : 2019-02-22 F. Acerbi
The paper shows that, contrary to what has been held since the sixteenth-century mathematician Christoph Clavius, there is no application of consequentia mirabilis (CM) in Greek mathematical works. This is shown by means of a detailed discussion of the logical structure of the proofs where CM is allegedly employed. The point is further enlarged to a critical assessment of the unsound methodology applied
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Michel Chasles’ foundational programme for geometry until the publication of his Aperçu historique Archive for History of Exact Sciences Pub Date : 2019-02-19 Paolo Bussotti
AbstractIn this paper, I propose the idea that the French mathematician Michel Chasles developed a foundational programme for geometry in the period 1827–1837. The basic concept behind the programme was to show that projective geometry is the foundation of the whole of geometry. In particular, the metric properties can be reduced to specific graphic properties. In the attempt to prove the validity
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Three thousand years of sexagesimal numbers in Mesopotamian mathematical texts Archive for History of Exact Sciences Pub Date : 2019-02-09 Jöran Friberg
The Mesopotamian system of sexagesimal counting numbers was based on the progressive series of units 1, 10, 1·60, 10·60, …. It may have been in use already before the invention of writing, with the mentioned units represented by various kinds of small clay tokens. After the invention of proto-cuneiform writing, c. 3300 BC, it continued to be used, with the successive units of the system represented
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Correction to: “The etherealization of common sense?” Arithmetical and algebraic modes of intelligibility in late Victorian mathematics of measurement Archive for History of Exact Sciences Pub Date : 2018-12-21 Daniel Jon Mitchell
The original version of this article unfortunately contained mistakes.
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Ptolemaic planetary models and Kepler’s laws Archive for History of Exact Sciences Pub Date : 2018-11-27 Christián C. Carman, Gonzalo L. Recio
Abstract In this article, we aim at presenting a thorough and comprehensive explanation of the mathematical and theoretical relation between all the aspects of Ptolemaic planetary models and their counterparts which are built according to Kepler’s first two laws (with optimized parameters). Our article also analyzes the predictive differences which arise from comparing Ptolemaic and these ideal Keplerian
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“The Etherealization of Common Sense?” Arithmetical and Algebraic Modes of Intelligibility in Late Victorian Mathematics of Measurement Archive for History of Exact Sciences Pub Date : 2018-11-10 Daniel Jon Mitchell
The late nineteenth century gradually witnessed a liberalization of the kinds of mathematical object and forms of mathematical reasoning permissible in physical argumentation. The construction of theories of units illustrates the slow and difficult spread of new “algebraic” modes of mathematical intelligibility, developed by leading mathematicians from the 1830s onwards, into elementary arithmetical
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Astronomical observations at the Maragha observatory in the 1260s–1270s Archive for History of Exact Sciences Pub Date : 2018-09-27 S. Mohammad Mozaffari
AbstractThis paper presents an analysis of the systematic astronomical observations performed by Muḥyī al-Dīn al-Maghribī (d. 1283 AD) at the Maragha observatory (northwestern Iran, ca. 1260–1320 AD) between 1262 and 1274 AD. In a treatise entitled Talkhīṣ al-majisṭī (Compendium of the Almagest), preserved in a unique copy at Leiden, Universiteitsbibliotheek (Or. 110), Muḥyī al-Dīn explains his observations
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A study of Babylonian planetary theory I. The outer planets Archive for History of Exact Sciences Pub Date : 2018-09-24 Teije de Jong
In this study I attempt to provide an answer to the question how the Babylonian scholars arrived at their mathematical theory of planetary motion. Although no texts are preserved in which the Babylonians tell us how they did it, from the surviving Astronomical Diaries we have a fairly complete picture of the nature of the observational material on which the scholars must have based their theory and
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The astronomical orientation of the historical Grand mosques in Anatolia (Turkey) Archive for History of Exact Sciences Pub Date : 2018-09-17 Mustafa Yilmaz, Ibrahim Tiryakioglu
In the ancient civilizations, the sky has been observed in order to understand the motions of the celestial bodies above the horizon. The study of faiths and practices dealing with the sky in the past has been attributed to the sun, the moon, and the prominent stars. The alignment and orientation of constructions to significant celestial objects were a common practice. The orientation was an important
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The end of an error: Bianchini, Regiomontanus, and the tabulation of stellar coordinates Archive for History of Exact Sciences Pub Date : 2018-08-21 Glen Van Brummelen
AbstractGiovanni Bianchini’s fifteenth-century Tabulae primi mobilis is a collection of 50 pages of canons and 100 pages of tables of spherical astronomy and mathematical astrology, beginning with a treatment of the conversion of stellar coordinates from ecliptic to equatorial. His new method corrects a long-standing error made by a number of his antecedents, and with his tables the computations are
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“A masterly though neglected work”, Boscovich’s treatise on conic sections Archive for History of Exact Sciences Pub Date : 2018-06-25 Andrea Del Centina, Alessandra Fiocca
In this paper, we describe the genesis of Boscovich’s Sectionum Conicarum Elementa and discuss the motivations which led him to write this work. Moreover, by analysing the structure of this treatise in some depth, we show how he developed the completely new idea of “eccentric circle” and derived the whole theory of conic sections by starting from it. We also comment on the reception of this treatise
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Uses of construction in problems and theorems in Euclid’s Elements I–VI Archive for History of Exact Sciences Pub Date : 2018-06-25 Nathan Sidoli
In this paper, I present an interpretation of the use of constructions in both the problems and theorems of Elements I–VI, in light of the concept of given as developed in the Data, that makes a distinction between the way that constructions are used in problems, problem-constructions, and the way that they are used in theorems and in the proofs of problems, proof-constructions. I begin by showing
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The concept of given in Greek mathematics Archive for History of Exact Sciences Pub Date : 2018-06-14 Nathan Sidoli
This paper is a contribution to our understanding of the technical concept of given in Greek mathematical texts. By working through mathematical arguments by Menaechmus, Euclid, Apollonius, Heron and Ptolemy, I elucidate the meaning of given in various mathematical practices. I next show how the concept of given is related to the terms discussed by Marinus in his philosophical discussion of Euclid’s
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François Viète’s revolution in algebra Archive for History of Exact Sciences Pub Date : 2018-04-16 Jeffrey A. Oaks
Françios Viète (1540–1603) was a geometer in search of better techniques for astronomical calculation. Through his theorem on angular sections he found a use for higher-dimensional geometric magnitudes which allowed him to create an algebra for geometry. We show that unlike traditional numerical algebra, the knowns and unknowns in Viète’s logistice speciosa are the relative sizes of non-arithmetized
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