Excerpt from A Treatise on the Theory of Algebraical Equations This supposition has been confirmed by the successive investigations of Geometers, who have shewn that the general solution of an equation whose coefficients are indeterminate, and whose roots have no particular relations to one another, is impossible beyond the fourth degree. It has also been shewn by Abel that, if two roots are so connected that one of them can be expressed rationally in terms of the other, the equation, if its degree be a prime number, is ...
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Excerpt from A Treatise on the Theory of Algebraical Equations This supposition has been confirmed by the successive investigations of Geometers, who have shewn that the general solution of an equation whose coefficients are indeterminate, and whose roots have no particular relations to one another, is impossible beyond the fourth degree. It has also been shewn by Abel that, if two roots are so connected that one of them can be expressed rationally in terms of the other, the equation, if its degree be a prime number, is solvable by radicals; and if a composite number, its solution depends on that of equations of inferior degrees. And more recently Gallois has demonstrated that, in order that an irreducible equation, whose degree is a prime number, may be solvable by radicals, it is necessary and sufficient that, any two of its roots being given, the others can be obtained rationally from them. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at ... This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
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