Archive for History of Exact Sciences

ISSNs: 0003-9519, 1432-0657

13 found

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  1.  2
    Einstein’s Second-Biggest Blunder: The Mistake in the 1936 Gravitational-Wave Manuscript of Albert Einstein and Nathan Rosen.Alexander S. Blum - 2022 - Archive for History of Exact Sciences 76 (6):623-632.
    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 use of a pathological coordinate transformation.
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  2. Desargues’s Concepts of Involution and Transversal, Their Origin, and Possible Sources of Inspiration.Andrea Del Centina - 2022 - Archive for History of Exact Sciences 76 (6):573-622.
    In this paper, we try to understand what considerations and possible sources of inspiration Desargues used to formulate his concepts of involution and transversal, and to state the related theorems that are at the basis of his Brouillon project. To this end, we trace some clues which are found scattered throughout his works, we connect them together in the light of his experience and knowledge in the field of perspective, and we investigate what were his motivations within Mersenne’s academy. As (...)
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  3.  3
    “The Language of Dirac’s Theory of Radiation”: The Inception and Initial Reception of a Tool for the Quantum Field Theorist.Markus Ehberger - 2022 - Archive for History of Exact Sciences 76 (6):531-571.
    In 1927, Paul Dirac first explicitly introduced the idea that electrodynamical processes can be evaluated by decomposing them into virtual, energy non-conserving subprocesses. This mode of reasoning structured a lot of the perturbative evaluations of quantum electrodynamics during the 1930s. Although the physical picture connected to Feynman diagrams is no longer based on energy non-conserving transitions but on off-shell particles, emission and absorption subprocesses still remain their fundamental constituents. This article will access the introduction and the initial reception of this (...)
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  4.  4
    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.Riccardo Bellé & Beatrice Sisana - 2022 - Archive for History of Exact Sciences 76 (5):471-511.
    The manuscript UCLA 170/624 contains Galileo’s proof of the center of gravity of the frustum of a cone, which was ultimately published as Theoremata circa centrum gravitatis solidorum in Discorsi e dimostrazioni matematiche intorno a due nuove scienze. The UCLA copy opens the possibility of giving a fuller account of Theoremata dating and development, and it can shed light on the origins of this research by the young Galileo. A comparison of the UCLA manuscript with the other extant copies is (...)
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  5.  8
    Felix Klein’s Projective Representations of the Groups $$S6$$ and $$A7$$.Henning Heller - 2022 - Archive for History of Exact Sciences 76 (5):431-470.
    This paper addresses an article by Felix Klein of 1886, in which he generalized his theory of polynomial equations of degree 5—comprehensively discussed in his Lectures on the Icosahedron two years earlier—to equations of degree 6 and 7. To do so, Klein used results previously established in line geometry. I review Klein’s 1886 article, its diverse mathematical background, and its place within the broader history of mathematics. I argue that the program advanced by this article, although historically overlooked due to (...)
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  6.  1
    A Mechanical Concentric Solar Model in Khāzinī’s Mu‘Tabar Zīj.S. Mohammad Mozaffari - 2022 - Archive for History of Exact Sciences 76 (5):513-529.
    The paper brings into light and discusses a concentric solar model briefly described in Chapter 5 of Section III of ‘Abd al-Raḥmān al-Khāzinī’s On experimental astronomy, a treatise embedded in the prolegomenon of his comprehensive Mu‘tabar zīj, completed about 1121 c.e. In it, the Sun is assumed to rotate on the circumference of a circle concentric with the Earth and coplanar with the ecliptic, but the motion of the vector joining the Earth and Sun is monitored by a small eccentric (...)
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  7. Brianchon and Poncelet’s Joint Memoir, the Nine-Point Circle, and Beyond.Andrea Del Centina - 2022 - Archive for History of Exact Sciences 76 (4):363-390.
    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 loci described by the centres of the conic sections required to pass through m points and to (...)
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  8.  1
    The Eclectic Content and Sources of Clavius’s Geometria Practica.John B. Little - 2022 - Archive for History of Exact Sciences 76 (4):391-424.
    We consider the Geometria Practica of Christopher Clavius, S.J., a surprisingly eclectic and comprehensive practical geometry text, whose first edition appeared in 1604. Our focus is on four particular sections from Books IV and VI where Clavius has either used his sources in an interesting way or where he has been uncharacteristically reticent about them. These include the treatments of Heron’s Formula, Archimedes’ Measurement of the Circle, four methods for constructing two mean proportionals between two lines, and finally an algorithm (...)
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  9.  1
    Gauss on Least-Squares and Maximum-Likelihood Estimation.Jan R. Magnus - 2022 - Archive for History of Exact Sciences 76 (4):425-430.
    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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  10. A Common-Sense Approach to the Problem of the Itinerary Stadion.Irina Tupikova - 2022 - Archive for History of Exact Sciences 76 (4):319-361.
    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 of the so-called itinerary stadion in antiquity. We discuss the possibility of using statistical analysis methods to estimate the length of the stadion by comparing (...)
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  11.  11
    Peirce’s Dragon-Head Logic.Minghui Ma & Ahti-Veikko Pietarinen - 2022 - Archive for History of Exact Sciences 76 (3):261-317.
    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 text, Peirce is seen to outline both a general theory of deduction and a general theory of consequence (...)
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  12.  5
    Vitali’s Generalized Absolute Differential Calculus.Alberto Cogliati - 2022 - Archive for History of Exact Sciences 76 (1):15-43.
    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 Pascal’s theory of forms and to providing an analysis of the process leading to a fully general notion of covariant derivative. Finally, the reception of (...)
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  13.  4
    An Alternative Interpretation of BM 76829: Astrological Schemes for Length of Life and Parts of the Body.John Steele - 2022 - Archive for History of Exact Sciences 76 (1):1-14.
    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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