NEW AND COMPLETE SYSTEM OF ARITHMETIC: INTENDED FOR THE USE OF SCHOOLS AND ACADEMIES. . BY CALEB ALEXANDER, A. M. AND ,” “ The Columbian Dictionary," An English, Latin, THIRD EDITION, REVISED AND CORRECTED ALBANY ; No. 45, State-Street. E. & E. Hosford-Printers, 1813. District of Massachusetts District, to wit: (L. S.) BE E IT REMEMBERED, That on the twenty eighth day of January, in the twenty-sixth year of the Independence of the United Sta:es of America, CALEB ALEXANDER, of the said District, hath deposited in this Office, the Title of a Book, the right whereof he claims as Author, in the words following, to wit: " A new and complete System of ARITHMETIC: intended for the use of Schools and Academies. By CALEB ALEXANDER, A. M. Author of " Virgil's Works, translated literally into prose The Columbian Dictionary--An English, Latin, and Greek Grammar-The young Gentlemen and Ladies' Instructor--and a Spelling Book on an improved plan-late Principal of Fairfield Academy, (N. Y.) now Preceptor of Onondaga Academy." In conformity to the Act of Congress of the United States, entitled “ An Act for the Encouragement of Learning, by securing the copies of Maps, Charts, and Books, to the Authors and Proprietors of such Copies, during the times therein 'mentioned.” N. GOODALE, Clerk of the District of Massachusetts Distric A true copy of Record, Attest. N. GOODALE, Clerk, W.L. Clement be. PREFACE. TO render the following system plain and easy, no pains have been spared. Treatises of this kind have often abounded with abstruse and intricate questions, more puzzling than beneficial to the learner. And some authors have dwelt too much on trifling questions, which, when understood, afford no useful knowledge. To shun these extremes, to feed the mind, and form our youth for active life, has been the principal aim, in this work. As the Federal mode of reckoning is well adapted to business, and is rapidly growing into use, particular attention has been given to this mode, in the rules under Decimal Fractions. To the patronage of a generous public, this work is humbly dedicated, by THE AUTHOR. Voor ARITHMETIC. SECTION 1. Explanation of Characters. +Sacstries Addition : as 4-75 make 9, Subtraction; as, 6-4 leaves to 8, so is 5 to 10. Equality; as, 4 and 7=11. Arithmetic is the art of computing by numbers, and is comprised in the five following rules, Numeration, Addition, Subtraction, Multiplication, and Division. NUMERATION Shows the different value of figures, as they may be differently arranged, and teaches how to read and write, by the following ten characters 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. The first is called a cypher; the rest, figures. The last pine are called significant figures, to distinguish them from the sypher, which of itself has no value. As it is placed, it may serve to increase or decrease the value of the figure or figures, with which it is connected. Thus, 4 is but cour. If the cypher be placed after it thus, 40, it becomes forty. When the cypher is placed before any figure, as in decimal arithmetic, it decreases the value of the figure. Thus, 4 in decimals, is only the 4 tenths of any thing. But when the cypher is placed be. fore it thus, 04, it becomes 4 hundredths of any thing. The nine figures have a certain, or an uncertain value. When they stand singly, or alone, their value is certain. Thus, 4, 5, 6, are but four, five, and six. If another figure be added, they are increased, in value, ten times. Thus 4, with 3 added, becomes 43 forty-three ; and 5, with 7 added, becomes 57 fifty-seven. This is called their uncertain yalue. Every figure, at the left hand, increases the value tenfold, in proportion to its distance from the right hand figure, or the place of units. Thus, 6 is six; 66 are sixty and six; 666 are six hundred, sixty, and six; 6666 are six thousand, six hun. A2 |