#### English Title

Solution of a problem requiring the rectification of an ellipse

#### Enestrom Number

52

#### Fuss Index

353

#### Original Language

Latin

#### English Summaries

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.

#### Published as

Journal article

#### Published Date

1741

#### Written Date

1735

#### Archive Notes

According to Eneström, Euler wrote a letter to Daniel Bernoulli in late 1734 indicating that he had solved the primary problem from this paper. See E864, p. 137.

#### Content Summary

Euler begins 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.

#### Record Created

2018-09-25

## Notes

According to Eneström, Euler wrote a letter to Daniel Bernoulli in late 1734 indicating that he had solved the primary problem from this paper. See ENE864, p. 137.