E52  Solutio problematum rectivicationem ellipsis requirentium
(Solution of a problem requiring the rectification of an ellipse)
Summary:
Euler starts with integrals of a certain form, which are really elliptical integrals, and derives secondorder
ordinary differential equations using the socalled “Modular equation” whose solution can be put back through the
given integral. Then several geometric problems are solved, which cause special cases of derived differential
equations to appear.
According to the records, it was presented to the St. Petersburg Academy on June 9, 1735.
Euler
had solved the problem dealt with in this treatise by the end of 1734. (See his letter to Daniel
Bernoulli, Bibl. math. 73, 1906/7, p. 140)
Publication:

Originally published in Commentarii academiae scientiarum Petropolitanae 8, 1741, pp. 8698

Opera Omnia: Series 1, Volume 20, pp. 8  20
 Reprinted in Comment. acad. sc. Petrop. 8, ed. nova, Bononiae 1752, pp. 7790 + 1 diagram
[52a]
Documents Available:
 Original publication: E052 (in the Commentarii)
 German translation (Artur Diener and Alexander Aycock): E052
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