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In the present edition, the questions referring to each section are ar ranged directly after the section, which generally brings the question and answer on the same page. This alteration will, no doubt, be found convenient to teachers.

A Key has also been prepared, in which all the questions contained in the Arithmetic are resolved, and in such a manner, that the par. ticular methods of solution can be fully understood. Many examples, not in the Arithmetic, have been imbodied in the Key, in order that the pupils may be exercised in questions not found in the books before them.

Since the publication of the last edition, a small introductory work has been prepared, entitled, “ First Lessons in Arithmetic:" in consequence of which, the “ Mental Arithmetic” which has heretofore formed the introduction, has been omitted.

Demonstrations of the rules for extracting the square and cube roots have also been added, and the Author now indulges the hope that no further changes will be found necessary.

The opinion of teachers has been so unanimous in favor of numerous examples as to induce the Author to add a Supplement, embracing near six hundred practical questions. These examples are arranged under heads corresponding with the order followed in the Arithmetic. One of the advantages resulting from this arrangement is, that the pupils of a class may be kept together—the more proficient being employed on the Supplement until the whole are ready to be advanced.

In deference to the opinions and wishes of many distinguished teachers, an edition of the Arithmetic has been prepared in which the answers to the questions are omitted. The edition, however, in which the answers are given to the alternate questions, is still published, and experience will show which method will best advance the interests of education.

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