English Title

Solution of a problem requiring the rectification of an ellipse

Authors

Leonhard Euler

Enestrom Number

52

Fuss Index

353

Original Language

Latin

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

Included in

Mathematics Commons

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