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  1.  37
    Interpreting the Infinitesimal Mathematics of Leibniz and Euler.Jacques Bair, Piotr Błaszczyk, Robert Ely, Valérie Henry, Vladimir Kanovei, Karin U. Katz, Mikhail G. Katz, Semen S. Kutateladze, Thomas McGaffey, Patrick Reeder, David M. Schaps, David Sherry & Steven Shnider - 2017 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 48 (2):195-238.
    We apply Benacerraf’s distinction between mathematical ontology and mathematical practice to examine contrasting interpretations of infinitesimal mathematics of the seventeenth and eighteenth century, in the work of Bos, Ferraro, Laugwitz, and others. We detect Weierstrass’s ghost behind some of the received historiography on Euler’s infinitesimal mathematics, as when Ferraro proposes to understand Euler in terms of a Weierstrassian notion of limit and Fraser declares classical analysis to be a “primary point of reference for understanding the eighteenth-century theories.” Meanwhile, scholars like (...)
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  2.  28
    Almost Equal: The Method of Adequality From Diophantus to Fermat and Beyond.Mikhail G. Katz, David M. Schaps & Steven Shnider - 2013 - Perspectives on Science 21 (3):283-324.
    Adequality, or παρισóτης (parisotēs) in the original Greek of Diophantus 1 , is a crucial step in Fermat’s method of finding maxima, minima, tangents, and solving other problems that a modern mathematician would solve using infinitesimal calculus. The method is presented in a series of short articles in Fermat’s collected works (1891, pp. 133–172). The first article, Methodus ad Disquirendam Maximam et Minimam 2 , opens with a summary of an algorithm for finding the maximum or minimum value of an (...)
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    Britton’s Theory of the Creation of Column $$\varPhi $$ Φ in Babylonian System A Lunar Theory.Steven Shnider - 2017 - Archive for History of Exact Sciences 71 (3):279-318.
    The following article has two parts. The first part recounts the history of a series of discoveries by Otto Neugebauer, Bartel van der Waerden, and Asger Aaboe which step by step uncovered the meaning of Column $$\varPhi $$ Φ, the mysterious leading column in Babylonian System A lunar tables. Their research revealed that Column $$\varPhi $$ Φ gives the length in days of the 223-month Saros eclipse cycle and explained the remarkable algebraic relations connecting Column $$\varPhi $$ Φ to other (...)
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