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  1.  42
    Medieval Arabic Algebra as an Artificial Language.Jeffrey A. Oaks - 2007 - Journal of Indian Philosophy 35 (5-6):543-575.
    Medieval Arabic algebra is a good example of an artificial language.Yet despite its abstract, formal structure, its utility was restricted to problem solving. Geometry was the branch of mathematics used for expressing theories. While algebra was an art concerned with finding specific unknown numbers, geometry dealtwith generalmagnitudes.Algebra did possess the generosity needed to raise it to a more theoretical level—in the ninth century Abū Kāmil reinterpreted the algebraic unknown “thing” to prove a general result. But mathematicians had no motive to (...)
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  2.  7
    Irrational “Coefficients” in Renaissance Algebra.Jeffrey A. Oaks - 2017 - Science in Context 30 (2):141-172.
    ArgumentFrom the time of al-Khwārizmī in the ninth century to the beginning of the sixteenth century algebraists did not allow irrational numbers to serve as coefficients. To multiply$\sqrt {18} $byx, for instance, the result was expressed as the rhetorical equivalent of$\sqrt {18{x^2}} $. The reason for this practice has to do with the premodern concept of a monomial. The coefficient, or “number,” of a term was thought of as how many of that term are present, and not as the scalar (...)
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  3.  19
    Algebraic Symbolism in Medieval Arabic Algebra.Jeffrey A. Oaks - 2012 - Philosophica 87:27-83.
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  4.  14
    Episodes in the Mathematics of Medieval Islam. J. L. Berggren.Jeffrey A. Oaks - 2017 - Nazariyat, Journal for the History of Islamic Philosophy and Sciences 4 (1):162-165.
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    Fibonacci’s De Practica Geometrie - by Barnabas Hughes.Jeffrey A. Oaks - 2009 - Centaurus 51 (2):168-169.
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    François Viète’s Revolution in Algebra.Jeffrey A. Oaks - 2018 - Archive for History of Exact Sciences 72 (3):245-302.
    Françios Viète was a geometer in search of better techniques for astronomical calculation. Through his theorem on angular sections he found a use for higher-dimensional geometric magnitudes which allowed him to create an algebra for geometry. We show that unlike traditional numerical algebra, the knowns and unknowns in Viète’s logistice speciosa are the relative sizes of non-arithmetized magnitudes in which the “calculations” must respect dimension. Along with this foundational shift Viète adopted a radically new notation based in Greek geometric equalities. (...)
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  7. Polynomials and Equations in Arabic Algebra.Jeffrey A. Oaks - 2009 - Archive for History of Exact Sciences 63 (2):169-203.
    It is shown in this article that the two sides of an equation in the medieval Arabic algebra are aggregations of the algebraic “numbers” with no operations present. Unlike an expression such as our 3x + 4, the Arabic polynomial “three things and four dirhams” is merely a collection of seven objects of two different types. Ideally, the two sides of an equation were polynomials so the Arabic algebraists preferred to work out all operations of the enunciation to a problem (...)
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