 | 1891 - 426 pagina’s
...cubic and biquadratic equations the auxiliary irrationalities which enter into the expressions for the roots are rationally expressible in terms of the roots of the given equation. The roots of the cubic equation, which we may, without loss of generality, assume in the reduced form... | |
 | 1891 - 430 pagina’s
...cubic and biquadratic equations the auxiliary irrationalities which enter into the expressions for the roots are rationally expressible in terms of the roots of the given equation. The roots of the cubic equation, which we may, without loss of generality, assume in the reduced form... | |
 | Leonard Eugene Dickson - 1903 - 142 pagina’s
...expressible in terms of the roots of }(x) = 0 and pth roots of unity. We therefore state Abel's Theorem: The solution of an algebraically solvable equation...the given equation and of certain roots of unity. The roots of an algebraically solvable equation can therefore be given a form such that all the radicals... | |
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The solution of an algebraically solvable equation can always be performed by a chain of binomial equations of prime degrees whose roots are rationally expressible in terms of the roots of the given equation and of certain roots of unity. 