A classic text on the abstract algebraic principles underlying polynomial equations, still relevant to modern mathematics. Hymers' clear and logical exposition is an essential resource for students of algebra and mathematics. This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

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 www.forgottenbooks.com 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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This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.