English Title

Inferences on the forms of roots of equations and of their orders

Authors

Leonhard Euler

Enestrom Number

30

Fuss Index

110

Original Language

Latin

Content Summary

For an equation of degree n, Euler wants to define a "resolvent equation" of degree n-1 whose roots are related to the roots of the original equation. Thus, by solving the resolvent one can solve the original equation. In sections 2 to 7, he works this out for quadratic, cubic, and biquadratic equations. In section 8, Euler says that he wants to try the same approach for solving the quintic equation and general nth degree equations. In the rest of the paper he tries to figure out in what cases resolvents will work.

Published as

Journal article

Published Date

1738

Written Date

1733

Original Source Citation

Commentarii academiae scientiarum Petropolitanae, Volume 6, pp. 216-231.

Opera Omnia Citation

Series 1, Volume 6, pp.1-19.

Record Created

2018-09-25

Included in

Mathematics Commons

Share

COinS