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In the preparation of the work, two objects have been kept con stantly in view:

1st. To make it educational; and,

2d. To make it practical.

To attain these ends, the following plan has been adopted:

1. To introduce every new idea to the mind of the pupil by a simple question, and then to express that idea in general terms under the from of a definition.

2. When a sufficient number of ideas are thus fixed in the mind, they are combined to form the basis of an analysis; so that all the principles are developed by analysis in their proper order.

3. An entire system of Mental Arithmetic has been carried forward with the text, by means of a series of connected questions placed at the bottom of each page; and if these, or their equivalents, are carefully put by the teacher, the pupil will understand the reasoning in evely process, and at the same time cultivate the powers of analysis and abstraction.

4. The work has been divided into sections, each containing a number of connected principles; and these sections constitute a series of dependent propositions that make up the entire system of principles and rules which the work develops.

Great pains have been taken to make the work PRACTICAL in its general character, by explaining and illustrating the various applications of Arithmetic in the transactions of business, and by connecting as closely as possible, every principle or rule, with all the applications which belong to it.

I have great pleasure in acknowledging my obligations to many teachers who have favored me with valuable suggestions in regard to the definitions, rules, and methods of illustration, in the previous editions. I hope they will find the present work free from the defects they have so kindly pointed out.

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