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"Entered according to act of Congress, the 11th of October, in the year 1832, by SAMUEL WARD, Junior, in the Office of the Clerk of the Southern District of New-York"

G. F. HOPKINS & SON, Printers, New-York.

© 12-27-4-0. HAT.



THE present Elementary Treatise is offered to the American public, with that confidence which its intrinsic merit and its highly flattering reception in England, serve to inspire.

At this time, when the great inquiry seems to be, how to facilitate the acquisition of knowledge by simplifying the means of its attainment, and by adapting them to the easy comprehension of the young and unskilled mind, a treatise which accomplishes this object in a high degree, will, undoubtedly, prove acceptable. The efforts of Mr. YOUNG, in this laudable field, have been directed to the improvement of the initiatory works on Mathematics, and have resulted in the production of a series of treatises of the greatest merit, among which his Algebra is one of the most prominent. This work possesses in a remarkable degree the merits of many of the best compilations now in use; and by thus combining their excellencies, and correcting the deficiencies of one by the worthiness of another, escapes their defects. Thus, the work of Lacroix, so replete with practical examples, would be preferred in respect of this circumstance to that of Bourdon; while on the other hand, it is inferior in regard to the theory of Algebra; but in the present work both are happily preserved. Indeed, in his unrivalled collection of Problems, in his beautiful demonstrations, especially of the Binomial Theorem, and in the elegance and perspicuity both of form and matter which he has observed, Mr. YOUNG has shown himself a complete master of the science, and to be entitled to the thanks of every true lover of the

analytical method. Instead of plodding through a dull and uninteresting volume, which begets a distaste for the science ere the novice has passed the portal, the student will here find much to amuse and to attract, and to generate an increased desire to become possessed of those noble instruments which may reveal to him the complete mechanism of the heavens.

In a work, however, which has accomplished so much, a few imperfections may be readily pardoned. The American Editor, in the discharge of his duty, has endeavoured to correct them, not only by drawing from his own resources, but by introducing sparingly the demonstrations of others. He has, moreover, taken great pains to preserve the text from typographical blemishes,* and therefore flatters himself that he has presented to the public an improved edition of the best treatise on Algebra now used. Some of these improvements may be here mentioned.

Throughout the Chapter on Simple Equations, there have been added new and original equations, and additional problems, involving one, two, and three unknown quantities, selected from the most recent publications, such as Bland's Algebraical Problems, the valuable collection of Meier Hirsch, and Wright's Supplement to Wood's Algebra. In Chapter III. an important alteration has been made, by transposing the subjects of Quadratic Equations and of Irrational Quantities; it being thought proper that the student should be made acquainted with the nature of Surds before he is called upon to employ them.

In addition to the Author's methods of solving Quadratic Equations, another has been given for the first time, on page 114, which will prove useful in preparing the student for his new method of solving Cubics and Equations of the higher orders; and in the same Chapter are added many rare problems in Quadratics. In Chapter

The Editor is particularly indebted for this correctness to Mr. Michael Floy, Junr., whose kind assistance in this part of his labours, and also in preparing the Chapters on Logarithms and on the Diophantine Analysis, he would here thankfully acknowledge.

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