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PROVIDENCE, October, 1826. THE undersigned have examined Mr. Roswell C. Smith's new Practical and Mental Arithmetic, designed to accompany Daboll's Arithmetic, and are satisfied that it is a plan admirably adapted to facilitate youth in their acquisition of this important branch of education ; and believing that its dissemination will be of great and perma. nent utility to the rising gerieration, they cheerfully recomniend it to the use of instructors and to the public patronage.

A. Woods, Prof. of Mathematics and Natural Philosophy.

G. A. DeWitt, One of the Principals of Provirlence High School.

Isaac HARTSHORN, Preceptor.

Moses Noves, Teacher of a School for young

DYAR T. HINCKLEY, Principal of Charles Field's street Academy.

CHARLES HENRY ALDEN, Preceptor at Olney Place.

Joseph L. Shaw, Westminster Academy.
LUTHER AINSWORTH, Teacher of Youth.

ORIGEN BACHELER, Preceptor of New Market Monitorial School.

Alfred RICKARD, Associate Prineipal of N. Main-Street Academy.



THE design of this work is to furnish in a concise, and intelligible form, a complete system of Practical Arithmetic, by questions and answers, both on the rules of operation, and the reasons of those rules : so that the juvenilo learner may proceed by a mental, rathor than a mechanical process; and be interested and profited by a study, in which he has usually been perplexed and disgusted.

The substance of the work was used in manuscript in my school, till the frequent transcribing became burdensome; and while preparing it for the press, for my own

several additions and improvements occurred, which it was thought would render it a work beneficial to the rising generation at large.

Among the many systems of Arithmetic in use, I have found none, by means of which the reasons of the various operations, the pupil is subjected to; is rendered sufficiently plain to him. Several recent publications display much ingenuity, but as a whole, contain too much of the merely curious, and too little of the useful. Some are not sufficiently conversant in the things to which Arithmetic is practically applied; and the pupil is even sent in. to Reduction, perhaps without the aid of the Tables of Weights, Coins, &c. where he makes much the same figure that the mariner would at sea, without his chart. A lack of rudimental examples, has likewise been a notori. ous defect; very closely allied to the last mentioned. Some authors, who have noticed this defect in the preface to their works, soom searcely to have thought of it after

wards. Some treatises contain questions on the Rules, with no answers annexed; and in order to find them, the pupil is despatched on a tour of discoveries in regions, “ Where forests of no meaning spread the page " In which all comprehension wanders, lost, bewildered;' and if among many laboured sentences, the phraseology of which is precisely as intelligible to him as the Hebrew, he happens to hit the lucky spot, of paper and ink, 'tis well; A throw with dice might have done the same. He treasures up the mysterious prizo, and is repaid with silly praise. Another pupil, who when challenged for his answer, should have the sense and spirit frankly to confess, " I can't find it, Sir," would be censured for au idler, or a dunce. The practice indeed of compelling scholars to learn by rote a tedious string of rules, which they are not made to understand the meaning and use of, is altogether preposterous; and would probably have been exploded long ago, but for the magisterial airs of knowing committees and still more knowing parents. If the time, wasted in this employment, were even spent in attempting to acquire the idioms of some foreign tongue, however hopeless the task, it might perhaps excite curiosity respecting other nations and thus prove of some little use.

Arithmetic has been sometimes accounted above the capacity of boys under 10 or 12 years of age ; and the profound and intricate science of language, the first principles of which are but with intense application,apprehended by the adult philosopher, have been sagely substituted as the more simple and pleasant exercise of infantile intel. lect. Arithmetic as usually taught it is confessed, is sufficiently intricate as the preceding observations imply.-At worst however it is obyiously better comprehended by children than English Grammar. And taught as it migbt be, it is thought to be better adapted to their age than any other study. Children necessarily begin the actwal use

of Arithmetic at an early period, in their sports and interchange of toys about the streets, and by a proper process, it is easy to make them see that the Arithmetic of books and schools is precisely of the same kind, as that which they use every day in buying apples and exchanging marbles.

The grand object is to convey instruction in language which they understand. Their knowledge of things is always greater than their knowledge of words, the signs of things. And of all studies of which they are capable, Arithmetic is best suited to exercise and expand their reasoning faculties. Such are the views with which this little volume is offered to the public.

The examples given for illustration and exercise, hava been borrowed from such things and occurrences as are familiar to children, the first being rendered as simple as possible, and gradually increasing in difficulty, to the last.

Federal Money is the eoin which has been principally used, as it is generally adopted by men of business throughout the Union.

A new and concise rule is given for computing Simp!. Interest, which is thought to deserve particular attention

The directions for stating Questions in the Rule of Three, are likewise different from any I have found in other books, and are thought to be an improvement.

Notes designed for instructors are interspersed throughout the book which will claim their careful perusal.

Fractions being simple in their nature and easily understood, are found among the ground rules, and are subsequently introduced sufficiently to answer all purposes of practical utility.

To avoid the embarrassment of abstruse and verbose expressions on the one hand and too much brevity on the other, has been unremittingly studied throughout the vol


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