达朗贝尔力挺无穷小的存在性
)力挺无穷小的存在性,促使数学分析到达一个历史“转折点”
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袁萌
附件:
1.4. J. D’Alembert and L. Carnot
A turning point in the history of the basic notions of analysis is associated with the ideas and activities of D’Alembert, one of the initiators and leading authors of the immortal masterpiece of the thought of the Age of Enlightenment, the French Encyclopedia or Explanatory Dictionary of Sciences, Arts, and Crafts. In the article “Dierential” he wrote: “Newton never considered dierential calculus to be some calculus of the innitely small, but he rather viewed it as the method of prime and ultimate ratios” [408, p. 157]. D’Alembert was the rst mathematician who declared that he had found the proof that the innitely small “do exist neither in Nature nor in the assumptions of geometricians” (a quotation from his article “Innitesimal” of 1759).
Excursus into the History of Calculus 7
The D’Alembert standpoint in Encyclopedia contributed much to the formulation by the end of the 18th century of the understanding of an innitesimal as a vanishing magnitude. It seems worthy to recall in this respect the book by Carnot Considerations on Metaphysics of the Innitely Small wherein he observed that “the notion of innitesimal is less clear than that of limit implying nothing else but the dierence between such a limit and the quantity whose ultimate value it provides.”