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PRACTICAL AND THEORETICAL

ARITHMETIC,

IN WHICH,

IN ADDITION TO THE USUAL MODES OF OPERATION, THE SCIENCL
OF NUMBERS, THE PRUSSIAN CANCELING SYSTEM, AND
OTHER IMPORTANT ABBREVIATIONS, HOLD

A PROMINENT PLACE.

BY HORATIO N. ROBINSON, A. M.

DESIGNED FOR SCHOOLS, COLLEGES, AND PRIVATE STUDENTS.

CINCINNATI:
PUBLISHED BY E. MORGAN & CO.

111 MAIN-ST.

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Entered according to Act of Congress, in the year 1845,

BY E. MORGAN & CO.,
In the Clerk's office for the District Court of Ohio.

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PRE FACE.

The public may very properly inquire, what good can be accomplished by adding another Arithmetic to the long list now in existence ? Both teachers and the taught are already sufficiently perplexed, in making a selection.

True, there are many arithmetics before us, claiming our attention; but more than half of them are more collections of questions, ordered to be solved by rules, given in a spiritless manner, having no connected system, and not recognizing the general and universal scientific character of numbers.

They place arithmetic before the mind of the pupil, as an art, not as a science they give him directions what to do, not what to think, and how to reason; and, in short, many of these books, now pressing for patronage, are already condemned by all good judges and scientific teachers.

Within the last ten or fifteen years, the science of arithmetic has undergone many changes, and received many important improvements; and such improvements have appeared, little by little, and from time to time-some in one book, and some in another-nowhere presenting one grand whole; and the object of this work is, to give unity and system to all the modern improvements which present practical utility, and interweave them in the common and general system, or such parts of it as are necessarily retained; and, how far we have accomplished this object, let the competent, the unprejudiced, and the uninterested, answer.

These modern improvements generally pass under the name of the canceling system; but canceling by no means includes them all, nor are they all included in numerical operationsprinciples, explanations, and forms, have been simplified and improved.

During the progress of investigation, there needs must be many fruitless attempts at improvement, and much useless matter must accumulate on the hands of original inquirers; and some such matter occasionally appears to the world, rather because it is singular, or new, than because it is practical

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