Analogy and the Growth of Mathematical Knowledge
Analogy and the Growth of Mathematical Knowledge
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类比与数学知识的增长
DOI：
10.1007/978-94-015-9558-2_20
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发表时间：
2000
影响因子：
1.7
通讯作者：
E. Knobloch
中科院分区：
文献类型：
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作者：
E. Knobloch
对像欧几里得或阿基米德这样的古代数学家的数学发现和严格论证的高度尊重，总是伴随着对他们到底是如何发现自己的结果的令人惊讶的猜测，这些结果后来以这样一种示范性的方式被证明，以至于它们成为严格论证的范式。因此，我们发现，开普勒以及莱布尼茨呼吁阿基米德的背景下的理由。更重要的是，莱布尼茨证明他的微分学（LMG 5，350）说，与阿基米德风格的区别只在于表达式（表达式），这在他的方法中更直接，更适合于发明艺术（art d'inventer）。他的微分只是一种新的符号，novum notationis genus（Leibniz 1714，404）。
High esteem for the mathematical discoveries and rigorous argumentation of the ancient mathematicians like Euclid or Archimedes has always been accompanied by astonished speculation about how after all they had found their results, which were subsequently demonstrated in such an exemplary way that they became paradigms of rigorous argumentation. Thus we find that Kepler as well as Leibniz appealed to Archimedes in the context of justification. What is more, Leibniz justified his differential calculus (LMG 5, 350) by saying that the difference from the style of Archimedes consists only in the expressions (expression), which in his method are more direct and more appropriate to the art of inventing (art d’inventer). His differential calculus is only a new kind of notation, novum notationis genus (Leibniz 1714, 404).