THE American Arithmetic, ADAPTED TO THE CURRENCY OF THE UNITED STATES. TO WHICH IS ADDED A CONCISE TREATISE ON THE MENSURATION OF PLANES AND SOLIDS. COMPILED FOR THE USE OF SCHOOLS &C. BY OLIVER WELCH, EXETER: Printed by C. NORRIS & Co. and sold at their Bookstore; 1812. " NEWHAMPSHIRE DISTRICT, to wit: BE IT REMEMBERED that on this thirteenth day of July, in the thirty seventh year of the Independence of the United States of America, OLIVER WELCH, of Exeter, in said district, hath deposited in this office the title of a book, whereof he claims the right as Author, in the following words, to wit...." THE AMERICAN ARITHMETIC, adapted to the currency of the United States, to which is added, a concise treatise on the Mensuration of Planes and Solids, Compiled for the use of schools, by OLIVER WELCH." In conformity to the Act of the Congress of the United States, entitled "An Act for the encouragement of learning, by securing copies of Maps, Charts and other books, to the Authors and Proprietors therein mentioned-And also " An Act for the encouragement of learning, by securing copies of Maps, Charts and other books, to the Authors and Proprietors therein mentioned, and extending the benefit thereof to the arts of Designing, Engraving and Etching historical and other prints. R. CUTTS SHANNON, A true copy of Record. Clerk of New-Hampshire District. Attest....R. CUTTS SHANNON, Clerk. 12-16-41. Recat 4-2-59 Sull 11-18-41 PREFACE MY principal design in publishing this book is to furnish Schools and Private Individuals with a concise system of Arithmetic, written in dollars and cents, connected with a treatise on Mensuration of Planes and Solids. The Arithmetical part I have made as concise as possible, have explained the rules in a very familiar manner, and have made such arrangement of them, as I have found by an experience of thirteen years, to be most likely to forward the learner; I have omitted many rules which are found in other books of this kind, that I might have more room to treat on Mensuration; on which, I have written as largely as the intended size of the book would permit. I trust that the candid reader will find the rules inserted in this book, which are not found in other arithmetics, to be much more necessary for the young learner to be acquainted with, than those which I have excluded. "One of the eastern Sages being asked what was most necessary for boys to learn; answered, what they ought to practice when they become men." Feeling desirous to promote the good of the Publick, by facilitating the education of youth, I have endeavoured to treat of nothing in this book, except what is really necessary for every young person to become acquainted with. I have treated of the method of making taxes, as is generally practised in the state of New Hampshire; and have added many other new problems in different parts of the work which will be useful and entertaining. I have spent much time, and been at no inconsiderable expense to render this book valuable to the risen, and rising generation; I sincerely hope that it may prove useful to the publick, and be worthy of their approbation and support. It has been fashionable in the publication of books of this kind, to introduce them into publick notice, through the influence of recommendations: but I think if a book has merits of its own, it will recommend itself; and if it has not merits of its own, it will not be supported even if others have recommended it. I have been at considerable trouble to have the copy carefully exainined by the Instructers of Schools, who highly approved of the work, and gave me liberty to make use of their names as recommenders; but having a desire that it might rise into notice by its own intrinsic value, I have submitted it to the publick without any other support than its own merits. Exeter, (N. H.) July 8, 1812. THE AUTHOR. THE AMERICAN ARITHMETIC, AND PRACTICAL MENSURATOR. ARITHMETIC is the art of computing by numbers; these numbers are called Figures, viz. 0, 1, 2, 3, 4, 5, 6, 7, 8,9,0, of itself has no value, but when joined to the right of other numbers, it increases their value in a tenfold proportion. Thus, I is one, 10 is ten, 2 is two, 20 is twenty. Of other Characters used in Arithmetic. Is the sign of Addition; and shews, that the number which follows the sign, must be added to the number before it. Thus 9+10 signifies that 9 and 10 are to be Added. Is the sign of Subtraction; and denotes the number fol. lowing it, must be subtracted from the one before it. Thus, 16-4 signifies that 4 must be taken from 16. > Is the sign of Multiplication; and denotes that all the numbers, between which it is placed, are to be multiplied together. Thus, 9 x9 signifies that 9 is to be multiplied by 9, or 9 x9x9 must be multiplied. Is the sign of Division; and denotes the number standing before it, is to be divided by the number following it. Thus, 93 signifies that is to be divided by 3. This is the sign of equality; and signifies the sum or product of the numbers before it, is equal to the number after it, 2+4+5=11 mean that 2, 4 and 5 added, their sum would be 11; and 2X4 X540 mean, that 2 and 4 multiplied, and that product multiplied again by 5 the |