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  1. 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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  2. 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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  3. 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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    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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  5. 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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  6. 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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