QUÍÐ MUNUS REIPUBLICÆ MAJUS MELIUSVE AFFERRE POSSUMUS, QUAM SI E VARIIS SUMENDUM EST OPTIMUM......CICERO. FOURTH EDITION; REVISED, CORRECTED, AND IMPROVED, PROFESSOR OF MATHEMATICKS, AND NATURAL PHILOSOPHY IN TROY, N. Y. PRINTED AND PUBLISHED BY WM. S. PARKER, SOLD AT THE TROY BOOKSTORE, AND BY THE PRINCIPAL BOOKSELLERS IN NORTHERN DISTRICT OF NEW YORK, TO WIT: BE IT REMEMBERED, That on the twenty first day of September, in the forty seventh year of the Independence of the United States of America, A. D. 1822, WILLIAM S. PARKER of the said District, has deposited in this Office the title of a Book, the right whereof he claims as proprietor, in the words following, to wit: "A new and comple system of Arithmetick, composed for the use of the citi. zens of the United States. By NICHOLAS PIKE, A. M. A. A. S. Quid munus reipublicæ majus meliusve afferre possumus, quam si juventutem docemus, et bene erudimus? E variis sumendum est optimum.-Cicero. Fourth Edition; revised, corrected, and improved, by CHESTer Dewey, a. A. s. Professor of Mathematicks, and Natural Philosophy in Williams College." In conformity to the act of the 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 ;" and also, to the act entitled "An act supplementary to an act 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,' and extending the benefits thereof to the arts of Designing, Engraving and Etching historical and other prints." RICHARD R. LANSING, Clerk of the Northern District of New York TO THE FIRST EDITION. IT may, perhaps, by some, be thought needless, when Authors are so multiplied, to attempt publishing any thing further on Arithmetick, as it may be imagined there can be nothing more than the repetition of a subject already exhausted. It is however the opinion of not a few, who are conspicuous for their knowledge in the Mathematicks, that the books, now in use among us, are gen erally deficient in the illustration and application of the rules; of the truth of which, the general complaint among Schoolmasters is a strong confirmation. And not only so, but as the United States are now an independent nation, it was judged that a System might be calculated more suitable to our meridian, than those heretofore published. Although I had sufficient reason to distrust my abilities for so arduous a task, yet not knowing any one who would take upon himself the trouble, and apprehending 1 could not render the publick more essential service, than by an attempt to remove the difficulties complained of, with diffidence I devoted myself to the work. I have availed myself of the best authors which could be obtained but have followed none particularly, except Bonnycastle's Method of Demonstration. Although I have arranged the work in such order as appeared to me the most regular and natural, the student is not obliged to pay a strict adherence to it; but may pass from one Rule to another, as his inclination or opportunity for study, may require. The Federal Coin, being purely decimal, most naturally falls in after Decimal Fractions. I have given several methods of extracting the Cube Root, and am indebted to a learned friend, who declines having his name made publick, for the investigation of two very concise Algebraick Theorems for the extraction of all Koots, and of a particular Theørem for the Sursolid. Among the Miscellaneous Questions, I have given some of a philosophical nature, as well with a view to inspire the pupil with a relish for philosophical studies, as to the usefulness of them in the common business of life. Being sensible the following Treatise will stand or fall, according to its real merit or demerit, I submit it to the judgment of the candid. With pleasure I embrace this opportunity, to express my gratitude to those learned Gentlemen, who have honoured this Treatise with their approbation, as well as to such Gentlemen, as have encouraged it by their subscriptions; and to request the reader to excuse any errours he may meet with; for although great pains have been taken in correcting, yet it is difficult to prevent errours from creeping into the press, and some may have escaped my own observation; in either case, a hint from the candid will much oblige their Most obedient, And humble Servant, THE AUTHOR |