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Treatise on Arithmetic:

THROUGH WHICH

THE ENTIRE SCIENCE CAN BE MOST EXPEDITIOUSLY

AND PERFECTLY LEARNED,

WITHOUT THE AID OF A TEACHER.

Designed for the Use of Schools and Pribate Students.

BY NOBLE HEATH.

DEO GENERIQUE HUMANO.

PHILADELPHIA:
T. ELLWOOD CHAPMAN, No. 1 S. FIFTH ST.

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Entered according to Act of Congress, in the year 1855, by

NOBLE HEATH, in the Clerk's Office of the District Court of the United States for the Eastern

District of Pennsylvania.

STEREOTYPED BY L, JOHNSON AND CO.

PHILADELPHIA.

1

PREFACE.

He who has, during the last forty years, been acquainted with the state of the science of Arithmetic, not only in the schools of this country, but in other parts, well knows that, at the commencement of that period, and for nearly half its duration, scarcely any thing better was found in the hands of the student than a miserable epitome or skeleton of the subject, presenting merely a few dogmas, followed by examples, without farther elucidation than the mechanical operation of one of these to serve as a model for the performance of all the others.

Divested almost entirely of scientific principles, Arithmetic was taught, in accordance with its title in the books then in use, as the art of computing by numbers; and a very clumsy, uninteresting, and wearisome art it was. Hence, the student, as might be expected, having no clue to the intricacies of the subject but memory, after ciphering through his Assistant,—as such a work was improperly called,—for the third, fourth, fifth, and even the sixth time, found himself almost as ignorant of the science as when he began.

Deeply felt and widely spread seem to have been the dissatisfaction, discouragement, and regret resulting from such palpable and enormous waste of the time and labour of the youth; for, during the last twenty years, new publications on this science, of much less exceptionable character, have, in the schools of Germany, France, England, and America, succeeded and superseded each other with surprising rapidity.

It is interesting to trace in these works the extremely gradual, yet steady approach toward a full development of the science, which, apparently, no one has hitherto dared to attempt.

The student who is early accustomed to investigation, in trac

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