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As someone reputed among certain historians to have given you the epsilon Cauchy startled me by using $\varepsilon$ to denote an infinitely small number in his 1826 text on differential geometry; see page 98 here:

[S]i l'on désigne par $\varepsilon$ un nombre infiniment petit, on aura $$ \frac{\sin\left(\frac{\pi}{2}\pm\varepsilon\right)}{r}= \frac{\sin(\pm\Delta\tau)}{\sqrt{\Delta x^2+\Delta y^2}} $$

Are there other instances of such nonweierstrassian usage by Cauchy?

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    $\begingroup$ Maybe Resumé (1823), 4ème Lecon, page 13: "Soient ... $i$ une quantité infiniment petite, et $h$ une quantité finie. Si l'on pose $i=\alpha x$, $\alpha$ sera encore une quantité infiniment petite, et l'on aura...$\dfrac {f(x+ \alpha h)-f(x)} { \alpha}$" where $i$ and $\alpha$ are used for "infinitesimal small" quantities. $\endgroup$ – Mauro ALLEGRANZA Jul 12 '17 at 15:08
  • $\begingroup$ Also on page 27 and 83 of this volume $\delta$ and $\epsilon$ appear as "nombres tres-petits" and as quantities differing "tres peu de zero". $\endgroup$ – Jan Peter Schäfermeyer Jul 17 '17 at 12:28

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