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“Such attempts lacked all semblance of mathematical rigor because of the lack at that time of satisfactory definitions of either the infinite of the infinitesimal. Arithmetic had not become sufficiently abstract and symbolic to free itself of spatial interpretations, for number was still interpreted metrically as a ratio of geometrical magnitudes.”

Carl B. Boyer, The History of the Calculus and Its Conceptual Development
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The History of the Calculus and Its Conceptual Development (Dover Books on Mathematics) The History of the Calculus and Its Conceptual Development by Carl B. Boyer
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