An Elementary Treatise On The Theory Of Equations

Reprint of the original, first published in 1861.

Excerpt from An Elementary Treatise on the Theory of Equations In this treatise it is my aim to give the elements of Determinants and the Theory of Equations in a form suitable, both in amount and quality of matter, for use in the undergraduate courses in our colleges and universities. To this end I have endeavored to make the work in every part readily intelligible to the average student who has become proficient in algebra and the elements of trigonometry. All use of the calculus has purposely been avoided. While the presentation of the subject has necessarily been condensed to suit the requirements of college courses, great pains has been taken not to sacrifice clearness to brevity. It is a short treatise, but not a syllabus. Part I treats of Determinants. The first two chapters give the fundamental theorems, with examples for illustration. The third chapter consists of applications and special forms of determinants, followed by a collection of carefully selected examples. These three chapters on determinants should serve as a helpful introduction to the study of this interesting class of functions. Part II treats of the Theory of Equations proper. The principal elementary theorems concerning algebraic and numerical equations arc deduced. After a brief introduction, giving definitions, etc., there follows a chapter on Complex Quantities, a subject which seems worthy of more space than is usually allotted to it in so elementary a treatise. 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.

Excerpt from An Elementary Treatise: On the Theory of Equations; With a Collection of Examples The present treatise contains all the propositions which are usually included in elementary treatises on the Theory of Equations, together with a collection of examples for exercise. As the Theory of Equations involves a large number of interesting and important results, which can be demonstrated with simplicity and clearness, the subject may advantageously engage the attention of a student at an early period of his mathematical course. The present treatise may be read by those who are familiar with Algebra, since no higher knowledge is assumed, except in Arts. 149, 175, 268, 308...314, and Chapter xxxi., which may be postponed by those who are not acquainted with De Moivre's Theorem in Trigonometry. This work may be regarded as a sequel to that on Algebra by the present writer, and accordingly the student has occasionally been referred to the treatise on Algebra for preliminary information on some topics here discussed. In composing the present work, the author has obtained assistance from the treatises on Algebra by Bourdon, Lefebure de Fourcy, and Mayer and Choquet; on special points he has consulted other writers, who are named in their appropriate places in the course of the work. The examples have been selected from the College and University examination papers, and the results have been given where it appeared necessary; in most cases however, from the nature of the example, the student will be able immediately to test the correctness of his result. 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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