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The present book is an enlargement of the authors' Elements of Algebra. To the end of Chapter XXVIII. it is identical with the latter and the School Algebra. Some revision of the later chapters in the Elements has been incorporated in this book, and a number of new chapters have been added.

The scope of the books, amply justified by their successful use in high and normal schools and colleges, is stated in the preface to the Elements :

“The aim has been to make the transition from ordinary Arithmetic to Algebra natural and easy. No efforts have been spared to present the subject in a simple and clear man

Yet nothing has been slighted or evaded, and all difficulties have been honestly faced and explained. New terms and ideas have been introduced only when the development of the subject made them necessary. Special attention has been paid to making clear the reason for every step taken. Each principle is first illustrated by particular examples, thus preparing the mind of the student to grasp the meaning of a formal statement of the principle and its proof. Directions for performing the different operations are, as a rule, given after these operations have been illustrated by particular examples.

“ The importance of mental discipline to every student of mathematics has also been fully recognized. On this account great care has been taken to develop the subject in a' logical


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