I read a bit of original Euler material on the elastica and Euler spiral for my PhD thesis [0] on interactive curve design, devoting two chapters to such history. I personally found it fascinating and beautiful.
So it's you! I read your thesis a few years ago, and recommended it to many people. I enjoyed the figures of elastica solutions with varying parameter, and I spend my time playing with spiro paths in inkscape; sometimes you get really wicked curves. Thank you so much, I love your work!
Anyone has suggestions on good papers in English translation from the archive? Here's one that is the first published proof of Fermat’s Little Theorem (link to translation at bottom of page):
Euler's first major work, the one that brought him fame, was his solution to the Basel problem (https://en.wikipedia.org/wiki/Basel_problem), when he was 28. Namely, he found the sum of the reciprocals of the squares of the integer, i.e. the value of the series (1 + 1/4 + 1/9 + 1/16 + ...), to be π²/6.
[0] http://levien.com/phd/phd.html