NOTICE TO TEACHERS.

Two years since, the Author of this book published a treatise on numbers, entitle "BOTHAM'S COMMON SCHOOL ARITHMETIC." It was received by the public with univer sal approbation, and has been very highly recommended by many eminent men, and ex perienced instructors. This fact induced the subscribers to believe that a Mental systen of Arithmetic, which would be a sure guide to WRITTEN, by the same author, could no fail of an unanimous approval-extensive circulation, and permanent support:-an would supply a desideratum, which has long existed in the publications of the day. Mr. Botham having devoted several years to the study of mathematics: to the teaching of arithmetic; and spent much time in the careful examination of treatises on Arith metic-and has for the last eighteen months had personal consultations with very many intelligent and popular teachers; trusts he apprehends their wants, and has produced a manual of Mental Arithmetic, which will be a sure guide to a system of WRIT TEN Arithmetic. He hopes he has rectified the misconceptions-corrected the errorsobviated the difficulties, and very materially improved on the works of others.

Fully sensible of the necessity of having an Arithmetic free from errors, the publish ers and author have spared no pains in making this book as correct as possible. The proof-sheets have been revised with particular care, and every example re-examined with renewed attention, before the Stereotype plates were permitted to go to press. It is be lieved" The only Sure Guide" will, in point of correctness of execution, bear a comparison with any Arithmetic ever published in the United States.

The Publishers submit this work to the judgment of their fellow citizens—and all they presume to ask for it, is, that no person will pass sentence upon it, until he shal have given it a patient and candid examination.

Entered according to Act of Congress, in the year 1835, by Clerk's Office of the District Court of Connecticut.

HENRY HILLS, in th

STEREOTYPED BY CONNER AND COOKE, NEW YORK.

5/21 37

PREFACE.

THIS Manual is especially intended for beginners. It is confined to Mental Arithmetic, with a view to prepare the pupil for exercises in WRITTEN Arithmetic. It is confidently believed, that it will accomplish the object. I have long wished that such a system might be published and introduced into common schools as a standard branch of education; and no good reason can be given, why the study of this most interesting and useful science should be confined to a peculiar season of the year, and only taught by men. The upper classes, at least, in district and private schools, might be profitably instructed in its elements, without neglecting any of those branches to which children usually attend.

This book contains many investigations, and new discoveries relative to the best methods of instruction, not to be found in any other similar production extant. I have selected such materials as are decidedly good, and unexceptionable, and arranged them in such a manner as may render the gradation easy. I have endeavored to make the entire work as plain and intelligible as possible. There is no danger that the BEGINNER will find the study of Arithmetic too easy; or that it will require so little mental exertion, as not to be retained. Let the arrangement be ever so politic-let the explanations be as full as they may, still the beginner will find difficulties enough to exercise his mind. His abilities are insufficient fully to comprehend a Rule; and his progress can be promoted only by his teacher, and by having examples, in abstract numbers, wrought out, or the different parts of the operations placed in a conspicuous manner. I have aimed to prepare a work, which any child of ten or twelve years of age, who is unacquainted with the rudiments of arithmetic, can understand, with the aid of a teacher. And from

VP

2-40

which he will be able to acquire a thorough knowledge of the primary rules, both in abstract and cCONCRETE numbers.

The following are the most important principles by which I have been governed in preparing this system of arithmetic :

To introduce only such parts of the science as properly belong to an elementary work: to adhere strictly to a methodical arrangement, that can be easily understood and remembered: never to anticipate principles, so as to make a clear understanding of the subject, depend upon some explanation which is to follow: to introduce every new principle distinctly by itself, that the pupil may encounter but one difficulty at a time: to deduce the rules, generally, from practical exercises, and to state them distinctly and in form: to give a variety of questions for solution under each rule: to solve and fully explain all questions which involve a new principle, or the new application of a principle already explained. And, finally, to advance from simple to more difficult problems, in such a manner, as may fully exercise the powers of the pupil without discouraging him.

As this book professes to be merely an introduction to, and exercises in Arithmetic-it was deemed sufficient not to extend it beyond the rule of Practice. It is presumed, that in its present form, it contains as much of Mental Arithmetic as would be proper or advantageous for young learners to study.

Whether I have succeeded in my plan or not, must be decided by teachers that a work of this kind is needed in the business of in- ! struction, particularly for BEGINNERS, and in summer schools, is acknowledged by them, and it is on this account, I claim the indulgence and patronage of parents, teachers, and friends to improvement. Hartford, May, 1835.

*

THE AUTHOR.

** The Author's Arithmetics are the only treatises that implicitly follow the orthography of Dr. WEBSTER; and agree with his "School Dictionary" and "Elementary Spelling Book."

N. B. My "Common School Arithmetic" contains 240 is for sale by the Booksellers in Hartford.

pages, and