EMBRACING ALSO THE THEORY AND APPLICATION OF LOGARITHMS; TOGETHER WITH AN APPENDIX, CONTAINING INFINITE SERIES, THE GENERAL THEORY OF EQUATIONS, AND THE MOST APPROVED METHODS OF RESOLVING THE HIGHER EQUATIONS. BY REV. DAVIS W. CLARK, A. M., PRINCIPAL OF AMENIA SEMINARY NEW-YORK: HARPER & BROTHERS, 82 CLIFF-STREET. Entered, according to Act of Congress, in the year 1843 by HARPER & BROTHERS, In the Clerk's Office of the Southern District of New-York. HOSP. BK. & NEWS. SOC. PRE FАСЕ. THE object of this treatise is to present to the student a full and systematic course of practical and theoretical elementary Algebra. With this object steadily in view, the author has made no effort for the display of mathematical genius, but has assiduously applied himself to the preparation of a text-book in the science. Believing that original discoveries are not best adapted to beginners, he has satisfied himself with the humble vocation of collecting, arranging, and illustrating the ample materials already provided. But it is due to himself to say that these materials have all been re-wrought, and not a few of them re-written several times. It has been a constant endeavour to make everything explicit, and also to exhibit it in the simplest possible form. By this means, the author has been enabled to embrace, within a comparatively small compass, a more comprehensive view of the science than can be found in any text-book on the subject now in use. Among the works which have shared, and still share most largely in the patronage of the public, isolated parts or subjects are treated with great ability and clearness; but, in some instances, these works are remarkably deficient, so far as concerns any methodical arrangement of the subjects introduced, while also other subjects of great importance are omitted altogether. That these books force their way into public patronage is not surprising, when, on the other hand, those treatises which are systematic in the arrangement of topics are, in general, too theoretical and abstract for the convenience or profit of the beginner, or, indeed, of the practical algebraist. In collecting his materials, the author has consulted the most approved writers upon the subject. It would be difficult, if not impossible, to point out the precise amount of his indebtedness to each; yet he does not hesitate to acknowledge it, nor has any desire of appearing original led him to remodel these materials. Indeed, this has been done only when it was necessary in order to preserve the unity of the work, or to render the subjects more explicit. In arranging and digesting these materials, however, the author has been fettered by no adopted system. Whatever seemed most appropriate to his general object, and in keeping with the general plan of his work, he has freely made use of, at all times having reference to the wants of our schools, and endeavouring to meet them. How far this object has been attained, he now leaves the reader to judge, claiming only for himself that it is a wellmeant contribution to elementary education in an important branch of science. For the article on "Roots of Numbers," as well as for other valuable assistance in the preparation of this work, he is indebted to the Rev. Joseph Cummings, A.B., lecturer on Natural Science in the Amenia Seminary. In the present work, Algebra has not been regarded merely as an introduction to the higher branches of mathematics, but also as a means of unfolding more clearly the principles and theory of common arithmetic. This is an important consideration. A great portion of the students in our academies and schools do not pursue the mathematical course beyond algebra. Such, aside from the mental discipline acquired in its study, derive their chief advantage from the superior understanding it gives them of common arithmetic; and we speak only the common sentiment of the better-informed schoolteachers, when we say that few, if any, are properly qualified to teach arithmetic without a knowledge of algebra. The author has not, however, limited himself to this object, and be |