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JAMES S. EATON, M. A.,
INSTRUCTOR IN PHILLIPS ACADEMY, ANDOVER, AND AUTROR OF
"EASY LESSONS IN MENTAL ARITHMETIC,” “THE COMMON
SCHOOL ARITHMETIC," AND "A TREATISE ON

WRITTEN ARITHMETIC."

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BOSTON:
THOMPSON, BIGELOW & BROWN

29 CORNHILL.

1871.

HARVARD
UNIVERSITY
LIBRARY

Entered, sccording to Act of Congress, in the year 1864, by

JAMES S. EATON, M.A., In he Cerk's Office of the District Court of the District of Massachusett

PREFACE.

Toz Pestalozzian or Inductive Method of teaching the science of numbers is now universally approved by intelligent teachers. The first attempt in this country to apply this method to Mental Arithmetic resulted in the publication of Colburn's First Lessons, a work whose success has not exceeded its merit. It was, however, a useful experiment rather than a perfect realization of the inductive system of instruction. That the subsequent books of the same class and purpose have failed to correct its defects, and thus meet the demand it created, is due evidently to their departure from the true theory as developed and exemplified by Pestalozzi.

The Author of this work has endeavored to improve upon all his predecessors, by adhering more closely than even Colburn did to the original method of the great Swiss educator, and by presenting at the same time, in a practical and attractive form, guch improvements in the application of his principles as have stood the test of enlightened experience.

In accordance with this design, the subjects are so arranged that each step of the learner prepares him for that which follows. By this suggestive and natural order of arrangement, together with copious illustrations of principles and applications by means of small concrete numbers, the pupil is led to a clear apprehension of the properties and relations of numbers, and

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