Solution of a problem requiring the rectification of an ellipse
Euler starts with integrals of a certain form, which are really elliptical integrals, and derives second-order ordinary differential equations using the so-called "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.
Original Source Citation
Commentarii academiae scientiarum Petropolitanae, Volume 8, pp. 86-98.
Opera Omnia Citation
Series 1, Volume 20, pp.8-20.