NUMBERS UNIVERSALIZED ΑΝ ADVANCED ALGEBRA BY DAVID M. SENSENIG, M. S. PROFESSOR OF MATHEMATICS, STATE NORMAL SCHOOL, WEST CHESTER, PA. COMPLETE NEW YORK: CINCINNATI CHICAGO FROM THE PRESS OF D. APPLETON & COMPANY PREFACE. NUMBERS UNIVERSALIZED is believed to embrace all algebraic subjects usually taught in the preparatory and scientific schools and colleges of this country. For convenience, it is divided into two parts, which are bound separately and together, to accommodate all kinds and grades of schools sufficiently advanced to adopt its use. Part First is intended as an advanced elementary algebra, and is especially adapted to schools preparing students for college, and to advanced classes in high and normal schools. In treatment, the great simplicity noticeable in the author's book for beginners, "Numbers Symbolized," has been avoided; yet care has been exercised to everywhere keep intact the logical sequence of thought, and to thus prevent the discussions from becoming unnecessarily abstruse and difficult. Definitions are logically arranged and expressed in simple, concise, and exact language. Illustrations are resorted to only when concepts described are not sufficiently clear without them. Fundamental principles and propositions are carefully formulated, and, whenever practicable, rigidly proved. Examples have been selected with special reference to variety in combination and methods of reduction. Unusual prominence is given to the subjects of factoring, radicals, and quadratic equations, as the author has learned by experience that few pupils entering classes in the higher mathematics are well enough drilled in these departments of work to follow with rapidity discussions involving them. The introduction into this part of the book of so much of indeterminate equations, loga |