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In this book the arithmetical basis of algebra is made prominent. In the earlier stages the formulæ and results are frequently tested by arithmetical applications, and in passing to new ideas numerical illustrations are often used. In this way the transition from arithmetic to algebra is gradually and easily made.

The authors have endeavored to present the subject of algebra as simply and clearly as is consistent with strict mathematical form. This is especially noticeable in the definitions and in the proofs of principles. The tendency of pupils to use symbols in a purely mechanical way is obviated as far as possible by the clear and concise manner in which the matter in elementary operations is presented.

This book is well adapted to schools in which the study of algebra is begun. It is especially fitted for use in high schools, academies, and other preparatory schools. It will be found that the simpler subjects of algebra are given a broader treatment than is usual in books of this grade; but by omitting the proofs of principles and the latter half of the exercises and problems an easier course is secured. The complete course is sufficiently full to meet the requirements for entrance into any college or university.

The large number and variety of the exercises, and the abundance and practical character of the problems, many of


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