Sinkiewicz, Galina Iwanowna On history of epsilontics. (English) Zbl 1429.01013 Antiq. Math. 10, 183-204 (2016). This paper reviews the development of epsilontics (\(\varepsilon\)-\(\delta\) language) in analysis out of the circle of ideas around continuity, limits, and infinitesimals. After a brief rehearsal of early ideas from Leibniz on, the author focuses on 19th-century mathematicians, especially Cauchy and Weierstrass. From a close reading of Cauchy’s Cours d’analyse (1821) and Calcul infinitésimal (1823) the author argues that Cauchy falls on the side of infinitesimals rather than proper limits, that the earliest appearance of limits and continuity in the \(\varepsilon\)-\(\delta\) language is in Weierstrass’s lecture notes of 1861, which he never edited or published, and that the definition of uniform continuity is due to Heine (1872). Then, Dini was the first to define continuity via left and right limits. Reviewer: Duncan J. Melville (Canton) Cited in 1 Document MSC: 01A55 History of mathematics in the 19th century 01A50 History of mathematics in the 18th century 01A60 History of mathematics in the 20th century Keywords:epsilon-delta language; continuity; limits; infinitesimals; epsilontics; Lagrange, Joseph-Louis; Ampère, André-Marie; Bolzano, Bernard; Heine, Eduard; Cantor, Georg; Lebesgue, Henri; Dini, Ulisse Biographic References: Cauchy, Augustin-Louis; Weierstrass, Karl PDFBibTeX XMLCite \textit{G. I. Sinkiewicz}, Antiq. Math. 10, 183--204 (2016; Zbl 1429.01013) Full Text: DOI References: [1] 200On history of epsilontics xkola, 1978. [2] [Ampére, 1806] A. Ampére. Recherches sur quelques points de la théorie des fonctions dérivées qui conduisent à une nouvelle démonstration de la série de Taylor et à l’expression nie des termes qu’on néglige lorsqu’on arrete cette sèrie á un terme quelconque. Mémoir par M. Ampére, Répétiteur à l’École Politechnique. 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