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THE unusual character of the recognition which the TEXTBOOK OF ALGEBRA, Part I., has received encourages the authors to believe that a book on the same lines, but in briefer form, will have a still wider field of usefulness. This book retains the distinctive features of the larger volume; but it is in many respects, for younger students, an improvement on the latter.

The needs of beginners have been constantly kept in mind. 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 manner. 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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