柯西与博尔扎诺之间的连续性：前因与优先性问题
Continuity between Cauchy and Bolzano: Issues of antecedents and priority
摘要：
在1970年发表的一篇论文中，格拉顿-吉尼斯认为柯西在他1821年出版的《分析教程》中可能抄袭了博尔扎诺1817年首次出版的《Rein analytischer Beweis》（RB）。这篇论文后来在几部著作中受到质疑，但其中的一些假设今天仍然盛行。特别是，它通常被认为是柯西没有发展他的概念的连续性功能之前，博尔扎诺制定了他在RB，这两个概念基本上是相同的。我们认为，这两个假设是不正确的，这是令人难以置信的，柯西的最初的见解，这一概念，最终演变成一种方法，使用无穷小，可以借用博尔扎诺的工作。此外，我们解释了博尔扎诺对这一概念的兴趣，并集中讨论了他对卡斯特纳定义的讨论（在他1766年著作的第183节），前者似乎至少部分地歪曲了这一定义。柯西对连续性的处理至少可以追溯到他1817年的课程摘要，驳斥了格拉顿-吉尼斯剽窃假说的一个关键组成部分（柯西可能是在1818年在巴黎图书馆阅读了RB之后从RB中提取了连续性）。我们探讨柯西和博尔扎诺连续性的前身在著作中的卡斯特纳和早期作者。
英文摘要：
In a paper published in 1970, Grattan-Guinness argued that Cauchy, in his 1821 book Cours d'Analyse, may have plagiarized Bolzano's book Rein analytischer Beweis (RB), first published in 1817. That paper was subsequently discredited in several works, but some of its assumptions still prevail today. In particular, it is usually considered that Cauchy did not develop his notion of the continuity of a function before Bolzano developed his in RB, and that both notions are essentially the same. We argue that both assumptions are incorrect, and that it is implausible that Cauchy's initial insight into that notion, which eventually evolved to an approach using infinitesimals, could have been borrowed from Bolzano's work. Furthermore, we account for Bolzano's interest in that notion and focus on his discussion of a definition by Kästner (in Section 183 of his 1766 book), which the former seems to have misrepresented at least partially. Cauchy's treatment of continuity goes back at least to his 1817 course summaries, refuting a key component of Grattan-Guinness' plagiarism hypothesis (that Cauchy may have lifted continuity from RB after reading it in a Paris library in 1818). We explore antecedents of Cauchy and Bolzano continuity in the writings of Kästner and earlier authors.
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