#### English Title

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

#### Enestrom Number

30

#### Fuss Index

110

#### Original Language

Latin

#### English Summaries

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 *n*th 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

#### 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 *n*th degree equations. In the rest of the paper he tries to figure out in what cases resolvents will work.

#### 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