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  1.  3
    Cracking Bones and Numbers: Solving the Enigma of Numerical Sequences on Ancient Chinese Artifacts.Andrea Bréard & Constance A. Cook - 2020 - Archive for History of Exact Sciences 74 (4):313-343.
    Numerous recent discoveries in China of ancient tombs have greatly increased our knowledge of ritual and religious practices. These discoveries include excavated oracle bones, bronze, jade, stone and pottery objects, and bamboo manuscripts dating from the twelfth to fourth century BCE. Inscribed upon these artifacts are a large number of records of numerical sequences, for which no explanation has been found of how they were produced. Structural links to the Book of Changes, a divination manual that entered the Confucian canon, (...)
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  2.  7
    How to Notate a Crossing of Strings? On Modesto Dedò’s Notation of Braids.Michael Friedman - 2020 - Archive for History of Exact Sciences 74 (4):281-312.
    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. Though the historical reasons for the success of Artin’s approach are known, a question arises as to whether other approaches to (...)
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  3.  2
    Poincaré’s Stated Motivations for Topology.Lizhen Ji & Chang Wang - 2020 - Archive for History of Exact Sciences 74 (4):381-400.
    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 concrete way.
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  4.  2
    On Qin Jiushao’s Writing System.Zhu Yiwen - 2020 - Archive for History of Exact Sciences 74 (4):345-379.
    The Mathematical Book in Nine Chapters, written by Qin Jiushao in 1247, is a masterpiece that is representative of Chinese mathematics at that time. Most of the previous studies have focused on its mathematical achievements, while few works have addressed the counting diagrams that Qin used as a writing system. Based on a seventeenth-century copy of Qin’s treatise, this paper systematically analyzes the writing system, which includes both a numeral system and a linear system. It argues that Qin provided a (...)
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  5.  2
    Borelli’s Edition of Books V–VII of Apollonius’s Conics, and Lemma 12 in Newton’s Principia.Alessandra Fiocca & Andrea Del Centina - 2020 - Archive for History of Exact Sciences 74 (3):255-279.
    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 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 by Borelli, with those of other authors, including that given by Newton himself. Moreover, after having (...)
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  6.  1
    The Principia’s Second Law (as Newton Understood It) From Galileo to Laplace.Bruce Pourciau - 2020 - Archive for History of Exact Sciences 74 (3):183-242.
    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, Lagrange, and Laplace—do not record, cite, discuss, or even mention the Principia’s statement of the second law. Nevertheless, the present study shows that all of these scientists do in fact assume the principle that the Principia’s second law (...)
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  7.  1
    A Proto-Normal Star Almanac Dating to the Reign of Artaxerxes III: BM 65156.John Steele - 2020 - Archive for History of Exact Sciences 74 (3):243-253.
    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 century BC onward. A small number of texts dating from before the third century present procedures for using the goal-year periods (...)
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  8.  3
    The Jalālī Calendar: The Enigma of its Radix Date.Hamid-Reza Giahi Yazdi - 2020 - Archive for History of Exact Sciences 74 (2):165-182.
    The Jalālī 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. /11th c. A.D. in Isfahan. After the death of Yazdigird III, the Yazdigirdī Calendar, as a solar one, gradually lost its position, and the Hijrī Calendar replaced it. After the rise of Islam, nonetheless, Iranians preferred various solar calendars to the Hijrī one. The Jalālī Calendar must be considered the culmination of such (...)
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  9.  1
    What Were the Genuine Banach Spaces in 1922? Reflection on Axiomatisation and Progression of the Mathematical Thought.Frédéric Jaëck - 2020 - Archive for History of Exact Sciences 74 (2):109-129.
    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 on the epistemological role of axioms. In particular, the notion of norm (...)
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  10.  1
    Une controverse entre Émile Picard et Leopold Kronecker.Cédric Vergnerie - 2020 - Archive for History of Exact Sciences 74 (2):131-164.
    Leopold Kronecker constructs in two articles published in 1869 and 1878, a theory which has its roots in Sturm’s work on the determination of the number of real solutions of an equation. The presentation of this theory of characteristics by Émile Picard will give rise to a controversy between the two mathematicians, who claimed the fame for a formula giving the number of solutions of certain systems of several equations. In this article, after an overview of the theory of characteristics, (...)
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  11.  2
    Deducing Newton’s Second Law From Relativity Principles: A Forgotten History.Olivier Darrigol - 2020 - Archive for History of Exact Sciences 74 (1):1-43.
    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, they employed continuous forces and a stronger relativity with respect to any commonly impressed motion. The name “principle of relative motions” and the (...)
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  12.  2
    The Law of Refraction and Kepler’s Heuristics.Juliana Gutiérrez Valderrama & Carlos Alberto Cardona Suárez - 2020 - Archive for History of Exact Sciences 74 (1):45-75.
    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, in this paper, we propose a model that agrees with Kepler’s heuristics and that is also successful in (...)
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  13.  1
    Lebesgue’s Criticism of Carl Neumann’s Method in Potential Theory.Ivan Netuka - 2020 - Archive for History of Exact Sciences 74 (1):77-108.
    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 confusion between the notions of infimum and minimum. The objective of this paper is to show that Lebesgue’s sharp criticism (...)
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