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Ibn al-Zarqālluh’s discovery of the annual equation of the Moon Archive for History of Exact Sciences (IF 0.5) Pub Date : 2024-02-02 S. Mohammad Mozaffari
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The new moon interval NA and the beginning of the Babylonian month Archive for History of Exact Sciences (IF 0.5) Pub Date : 2024-01-28
Abstract This study examines Babylonian records of the new moon interval NA (sunset to moonset on the day of first lunar visibility) and the connection of this interval to the length of the moon. I show that the NA intervals in the Normal Star Almanacs were computed using the goal-year method and were then used in turn to predict the lengths of each month of the year. I further argue that these predicted
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Lewis Caerleon and the equation of time: tabular astronomical practices in late fifteenth-century England Archive for History of Exact Sciences (IF 0.5) Pub Date : 2024-01-25 Laure Miolo, Stefan Zieme
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Francesco Fontana (1580–1656) from practice to rules of calculation of lens systems Archive for History of Exact Sciences (IF 0.5) Pub Date : 2023-11-14 Yaakov Zik, Giora Hon
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The efflux problem: how hydraulics became divorced from hydrodynamics Archive for History of Exact Sciences (IF 0.5) Pub Date : 2023-11-07 Michael Eckert
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Levi-Civita simplifies Einstein. The Ricci rotation coefficients and unified field theories Archive for History of Exact Sciences (IF 0.5) Pub Date : 2023-10-25 Franco Cardin, Rossana Tazzioli
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
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Tables for the radii of the Sun, the Moon, and the shadow from John of Gmunden to Longomontanus Archive for History of Exact Sciences (IF 0.5) Pub Date : 2023-09-26 Bernard R. Goldstein, José Chabás
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Geographic longitude in Latin Europe during the twelfth and thirteenth centuries Archive for History of Exact Sciences (IF 0.5) Pub Date : 2023-09-13 C. Philipp E. Nothaft
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
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Galois and the simple group of order 60 Archive for History of Exact Sciences (IF 0.5) Pub Date : 2023-09-07 Ian Stewart
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The Helmholtz legacy in color metrics: Schrödinger’s color theory Archive for History of Exact Sciences (IF 0.5) Pub Date : 2023-08-29 Valentina Roberti, Giulio Peruzzi
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Hero and the tradition of the circle segment Archive for History of Exact Sciences (IF 0.5) Pub Date : 2023-07-24 Henry Mendell
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Auerbach, Lotka, and Zipf: pioneers of power-law city-size distributions Archive for History of Exact Sciences (IF 0.5) Pub Date : 2023-07-14 Diego Rybski, Antonio Ciccone
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An early system A-type scheme for Saturn from Babylon Archive for History of Exact Sciences (IF 0.5) Pub Date : 2023-06-20 John Steele, Teije de Jong
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Eudoxus’ simultaneous risings and settings Archive for History of Exact Sciences (IF 0.5) Pub Date : 2023-06-14 Francesca Schironi
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Geometry and analysis in Anastácio da Cunha’s calculus Archive for History of Exact Sciences (IF 0.5) Pub Date : 2023-06-08 João Caramalho Domingues
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Measurements of altitude and geographic latitude in Latin astronomy, 1100–1300 Archive for History of Exact Sciences (IF 0.5) Pub Date : 2023-06-06 C. Philipp E. Nothaft
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The Jeffreys–Lindley paradox: an exchange Archive for History of Exact Sciences (IF 0.5) Pub Date : 2023-05-30 Jeremy Gray, Joshua L. Cherry, Eric-Jan Wagenmakers, Alexander Ly
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Federico Commandino and the Latin edition of Apollonius’s Conics (1566) Archive for History of Exact Sciences (IF 0.5) Pub Date : 2023-03-20 Argante Ciocci
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Felix Klein, Sophus Lie, contact transformations, and connexes Archive for History of Exact Sciences (IF 0.5) Pub Date : 2023-03-09 L. D. Kay
Much of the mathematics with which Felix Klein and Sophus Lie are now associated (Klein’s Erlangen Program and Lie’s theory of transformation groups) is rooted in ideas they developed in their early work: the consideration of geometric objects or properties preserved by systems of transformations. As early as 1870, Lie studied particular examples of what he later called contact transformations, which
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Ptolemy’s treatise on the meteoroscope recovered Archive for History of Exact Sciences (IF 0.5) Pub Date : 2023-03-09 Victor Gysembergh, Alexander Jones, Emanuel Zingg, Pascal Cotte, Salvatore Apicella
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SHAKE and the exact constraint satisfaction of the dynamics of semi-rigid molecules in Cartesian coordinates, 1973–1977 Archive for History of Exact Sciences (IF 0.5) Pub Date : 2023-02-21 Daniele Macuglia
This essay traces the history of early molecular dynamics simulations, specifically exploring the development of SHAKE, a constraint-based technique devised in 1976 by Jean-Paul Ryckaert, Giovanni Ciccotti and the late Herman Berendsen at CECAM (Centre Européen de Calcul Atomique et Moléculaire). The work of the three scientists proved to be instrumental in giving impetus to the MD simulation of complex
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Canonical transformations from Jacobi to Whittaker Archive for History of Exact Sciences (IF 0.5) Pub Date : 2023-01-31 Craig Fraser, Michiyo Nakane
The idea of a canonical transformation emerged in 1837 in the course of Carl Jacobi's researches in analytical dynamics. To understand Jacobi's moment of discovery it is necessary to examine some background, especially the work of Joseph Lagrange and Siméon Poisson on the variation of arbitrary constants as well as some of the dynamical discoveries of William Rowan Hamilton. Significant figures following
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Helmholtz and the geometry of color space: gestation and development of Helmholtz’s line element Archive for History of Exact Sciences (IF 0.5) Pub Date : 2023-01-17 Giulio Peruzzi, Valentina Roberti
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Joseph Ibn Waqār and the treatment of retrograde motion in the middle ages Archive for History of Exact Sciences (IF 0.5) Pub Date : 2023-01-06 Bernard R. Goldstein, José Chabás
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On fluidity of the textual transmission in Abraham bar Hiyya’s Ḥibbur ha-Meshiḥah ve-ha-Tishboret Archive for History of Exact Sciences (IF 0.5) Pub Date : 2022-10-20 Michael Friedman, David Garber
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A terminological history of early elementary particle physics Archive for History of Exact Sciences (IF 0.5) Pub Date : 2022-09-21 Helge Kragh
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History and nature of the Jeffreys–Lindley paradox Archive for History of Exact Sciences (IF 0.5) Pub Date : 2022-08-26 Eric-Jan Wagenmakers, Alexander Ly
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Einstein’s second-biggest blunder: the mistake in the 1936 gravitational-wave manuscript of Albert Einstein and Nathan Rosen Archive for History of Exact Sciences (IF 0.5) Pub Date : 2022-08-25 Alexander S. Blum
In a 1936 manuscript submitted to the Physical Review, Albert Einstein and Nathan Rosen famously claimed that gravitational waves do not exist. It has generally been assumed that there was a conceptual error underlying this fallacious claim. It will be shown, through a detailed study of the extant referee report, that this claim was probably only the result of a calculational error, the accidental
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Desargues’s concepts of involution and transversal, their origin, and possible sources of inspiration Archive for History of Exact Sciences (IF 0.5) Pub Date : 2022-08-10 Andrea Del Centina
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“The language of Dirac’s theory of radiation”: the inception and initial reception of a tool for the quantum field theorist Archive for History of Exact Sciences (IF 0.5) Pub Date : 2022-07-05 Markus Ehberger
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Federico Commandino and his Latin edition of Aristarchus’s On the Sizes and Distances of the Sun and the Moon Archive for History of Exact Sciences (IF 0.5) Pub Date : 2022-06-29 Argante Ciocci
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A mechanical concentric solar model in Khāzinī’s Mu‘tabar zīj Archive for History of Exact Sciences (IF 0.5) Pub Date : 2022-06-11 S. Mohammad Mozaffari
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The eclectic content and sources of Clavius’s Geometria Practica Archive for History of Exact Sciences (IF 0.5) Pub Date : 2022-05-13 John B. Little
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Galileo Galilei and the centers of gravity of solids: a reconstruction based on a newly discovered version of the conical frustum contained in manuscript UCLA 170/624 Archive for History of Exact Sciences (IF 0.5) Pub Date : 2022-04-28 Riccardo Bellé, Beatrice Sisana
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Felix Klein’s projective representations of the groups $$S_6$$ S 6 and $$A_7$$ A 7 Archive for History of Exact Sciences (IF 0.5) Pub Date : 2022-04-25 Henning Heller
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Gauss on least-squares and maximum-likelihood estimation Archive for History of Exact Sciences (IF 0.5) Pub Date : 2022-04-02 Jan R. Magnus
Gauss’ 1809 discussion of least squares, which can be viewed as the beginning of mathematical statistics, is reviewed. The general consensus seems to be that Gauss’ arguments are at fault, but we show that his reasoning is in fact correct, given his self-imposed restrictions, and persuasive without these restrictions.
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Brianchon and Poncelet’s joint memoir, the nine-point circle, and beyond Archive for History of Exact Sciences (IF 0.5) Pub Date : 2022-03-08 Andrea Del Centina
In this paper, we give a thorough account of Brianchon and Poncelet’s joint memoir on equilateral hyperbolas subject to four given conditions, focusing on the most significant theorems expounded therein, and the determination of the “nine-point circle”. We also discuss about the origin of this very rare example of collaborative work for the time, and the general challenge of finding the nature of the
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A common-sense approach to the problem of the itinerary stadion Archive for History of Exact Sciences (IF 0.5) Pub Date : 2022-03-03 Irina Tupikova
Estimating the length of the Greek stadion remains controversial. This paper highlights the pitfalls of a purely metrological approach to this problem and proposes a formal differentiation between metrologically defined ancient measuring units and other measures used to estimate long distances. The common-sense approach to the problem is strengthened by some cross-over documentary evidence for usage
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Peirce’s Dragon-Head Logic (R 501, 1901) Archive for History of Exact Sciences (IF 0.5) Pub Date : 2022-02-24 Minghui Ma, Ahti-Veikko Pietarinen
Peirce wrote in late 1901 a text on formal logic using a special Dragon-Head and Dragon-Tail notation in order to express the relation of logical consequence and its properties. These texts have not been referred to in the literature before. We provide a complete reconstruction and transcription of these previously unpublished sets of manuscript sheets and analyse their main content. In the reconstructed
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Federico Commandino and the Latin edition of Pappus’ Collection Archive for History of Exact Sciences (IF 0.5) Pub Date : 2021-11-21 Argante Ciocci
The Latin edition of the Mathematicae Collectiones was published in print in 1588, thirteen years after Federico Commandino’s demise. For his Latin version of Pappus’s work, Comandino used two Greek codices, formerly identified by Treweek. In this article, another Greek manuscript, revised and annotated by Commandino, is revealed. Two letters from Commandino to Ettore Ausonio shed new light on the
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Poincaré’s works leading to the Poincaré conjecture Archive for History of Exact Sciences (IF 0.5) Pub Date : 2021-10-13 Lizhen Ji, Chang Wang
In the last decade, the Poincaré conjecture has probably been the most famous statement among all the contributions of Poincaré to the mathematics community. There have been many papers and books that describe various attempts and the final works of Perelman leading to a positive solution to the conjecture, but the evolution of Poincaré’s works leading to this conjecture has not been carefully discussed
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Nombrils, bruslans, autrement foyerz: la géométrie projective en action dans le Brouillon Project de Girard Desargues Archive for History of Exact Sciences (IF 0.5) Pub Date : 2021-09-16 Anglade, Marie, Briend, Jean-Yves
In the middle part of his Brouillon Project on conics, Girard Desargues develops the theory of the traversale, a notion that generalizes the Apollonian diameter and allows to give a unified treatment of the three kinds of conics. We showed elsewhere that it leads Desargues to a complete theory of projective polarity for conics. The present article, which shall close our study of the Brouillon Project
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The Archimedean ‘sambukē’ of Damis in Biton Archive for History of Exact Sciences (IF 0.5) Pub Date : 2021-09-08 Keyser, Paul T.
Biton’s Construction of Machines of War and Catapults describes six machines by five engineers or inventors; the fourth machine is a rolling elevatable scaling ladder, named sambukē, designed by one Damis of Kolophōn. The first sambukē was invented by Herakleides of Taras, in 214 BCE, for the Roman siege of Syracuse. Biton is often dismissed as incomprehensible or preposterous. I here argue that the
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Euler first theory of resonance Archive for History of Exact Sciences (IF 0.5) Pub Date : 2021-07-10 Sylvio R. Bistafa
We examine a publication by Euler, De novo genere oscillationum, written in 1739 and published in 1750, in which he derived for the first time, the differential equation of the (undamped) simple harmonic oscillator under harmonic excitation, namely the motion of an object acted on by two forces, one proportional to the distance traveled, the other varying sinusoidally with time. He then developed a
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Carnot’s theory of transversals and its applications by Servois and Brianchon: the awakening of synthetic geometry in France Archive for History of Exact Sciences (IF 0.5) Pub Date : 2021-06-08 Andrea Del Centina
In this paper we discuss in some depth the main theorems pertaining to Carnot’s theory of transversals, their initial reception by Servois, and the applications that Brianchon made of them to the theory of conic sections. The contributions of these authors brought the long-forgotten theorems of Desargues and Pascal fully to light, renewed the interest in synthetic geometry in France, and prepared the
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Vitali’s generalized absolute differential calculus Archive for History of Exact Sciences (IF 0.5) Pub Date : 2021-05-24 Alberto Cogliati
The paper provides an analysis of Giuseppe Vitali’s contributions to differential geometry over the period 1923–1932. In particular, Vitali’s ambitious project of elaborating a generalized differential calculus regarded as an extension of Ricci-Curbastro tensor calculus is discussed in some detail. Special attention is paid to describing the origin of Vitali’s calculus within the context of Ernesto
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An alternative interpretation of BM 76829: astrological schemes for length of life and parts of the body Archive for History of Exact Sciences (IF 0.5) Pub Date : 2021-05-20 John Steele
In this paper I present an alternative reading and interpretation of the cuneiform tablet BM 76829. I suggest that the obverse of the tablet contains a simple astrological scheme linking the sign of the zodiac in which a child is born to the maximum length of life, and that the reverse contains a copy of a scheme relating parts of the body to the signs of the zodiac.
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Mathématiques en perspective: Desargues, la Hire, le Poîvre Archive for History of Exact Sciences (IF 0.5) Pub Date : 2021-05-18 Jean-Yves Briend
Il est tentant de considérer l’œuvre mathématique de Girard Desargues, plus particulièrement son Brouillon Project sur les coniques, comme un travail de mathématiques appliquées à l’art de la perspective. Nous voudrions montrer dans cet article qu’il est sans doute plus pertinent de considérer que Desargues fait des mathématiques en praticien de la perspective ou, plus précisément, que son œuvre peut
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David Hilbert and the foundations of the theory of plane area Archive for History of Exact Sciences (IF 0.5) Pub Date : 2021-05-05 Eduardo N. Giovannini
This paper provides a detailed study of David Hilbert’s axiomatization of the theory of plane area, in the classical monograph Foundation of Geometry (1899). On the one hand, we offer a precise contextualization of this theory by considering it against its nineteenth-century geometrical background. Specifically, we examine some crucial steps in the emergence of the modern theory of geometrical equivalence
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Fiction, possibility and impossibility: three kinds of mathematical fictions in Leibniz’s work Archive for History of Exact Sciences (IF 0.5) Pub Date : 2021-04-24 Oscar M. Esquisabel, Federico Raffo Quintana
This paper is concerned with the status of mathematical fictions in Leibniz’s work and especially with infinitary quantities as fictions. Thus, it is maintained that mathematical fictions constitute a kind of symbolic notion that implies various degrees of impossibility. With this framework, different kinds of notions of possibility and impossibility are proposed, reviewing the usual interpretation
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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 0.5) 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 (IF 0.5) 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 (IF 0.5) 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 (IF 0.5) 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 (IF 0.5) 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 (IF 0.5) 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 (IF 0.5) 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 (IF 0.5) 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 (IF 0.5) 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 (IF 0.5) 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