i SYSTEM OF ARITHMETICK. COMPOSED FOR THE USE OF THE CITIZENS OF THE United States. 4 BY NICOLAS PIKE, A. M. A. A. S. QUID MUNUS REIPUBLICE MAJUS MELIUSVE AFFERRE POSSUMUS, QUAM SI JU- VENTUTEM DOCEMUS, ET BENE ERUDIMUS? E VARIIS SUMENDUM EST OPTIMUM.... CICERO, THIRD EDITION. REVISED, CORRECTED AND IMPROVED, AND MORE PARTICULARLY ADAPTED BY NATHANIEL LORD, A. M. PUBLISHED BY THOMAS & ANDREW's, Proprietors of the Copy-Right.-Sold at their Bookstore, No. 45, Newbury- APRIL, 1808 1. T. BUCKINGHAM, PRINTER.. DISTRICT OF MASSACHUSETTS, TO WIT : BE it remembered, that on the thirty first day of March, in the thirty second year of the Independence of the United States of America, THOMAS & ANDREWS, of the faid district, have depofited in this office the Title of a Book, the Right whereof they claim as Proprietors, in the Words following, to wit: "A New and Complete System of Arithmetick, composed for the use of the citizens of the United States. By NICOLAS PIKE, A. M. A. A. S. Quid munus reipublica majus meliufve afferre poffumus, quam fi juventutem docemus, et bene erudimus. -E variis fumendum eft optimum.-Cicero. Third Edition. Revised, Corrected, and Improved, and more particularly adapted to the Federal Currency. By NATHANIEL LORD, А. м." In conformity to the Act of the Congress of the United States, intitled, " An Act for the Encouragement of Learning, by securing the Copies of Maps, Charts and Books, to the Authors and Proprietors of fuch Copies, during the times therein mentioned;" and also to an Act intitled, " An Act supplementary to An Act, intitled, 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." WM. SMITH SHAW, Clerk of the District of Massachusetts Dartmouth University, A. D. 1786. AT the request of Nicolas Pike, Efq. we have inspected his System of Arithmetick, which we cheerfully recommend to the publick, as eafy, accurate, and complete. And we apprehend there is no treatise of the kind extant, from which fo great utility may arife to Schools. B. WOODWARD, Math. and Phil. Prof. I do most sfincerely concur in the preceding recommendation. it this Providence, State of Rhode Island, 1785. WHOEVER may have the perusal of this treatise on Arithmetick may naturally conclude İ might have fpa spared myself the trouble of giving recommendation, as the work will speak more for itself than the most elaborate recommendation from my pen can speak for it: But as I have always been much delighted with the contemplation of mathematical fubjects, and at the fame time fully sensible of the utility of a work of this nature, was willing to render every assistance in my power to bring it to the publick view: And should the student read it with the fame pleasure with which I perused the sheets before they went to the press, am perfuaded he will not fail of reaping that benefit from it which he may expect, or wish for, to fatisty his curiofity in a subject of this nature. The author, in treating on numbers, has done it with fo much perfpicuity and fingular address, that I am convinced the study thereof will become more a ple pleasure than a tafk. The arrangement of the work, and the method by which he leads the tyro into the first principles of numbers, are novelties I have not met with in any book I have seen. Wingate, Hatton, Ward, Hill, and many other authors, whose names might be adduced, if necessary, have claimed a confiderable share of merit; but when brought into a comparative point of view with this treatife, they are inadequate and defective. This volume contains, befides what is useful and necessary in the common affairs of life, a great fund for amufement and entertainment. The Mechanick will find in it much more than he may have occafion for; the Lawyer, Merchant and Mathematician, will find an ample field for the exercise of their genius; and am well assured it may be read to great advantage by students of every class, from the lowest school to the University. More than this need not be faid by me, and to have faid less, would be keeping back a tribute justly due to the merit of this work. BENJAMIN WEST. University in Cambridge, A. D. 1786. HAVING, by the defire of Nicolas Pike, Efq. inspected the following vol. ume in manufcript, we beg leave to acquaint the publick, that in our opinion it is a work well executed, and contains a complete system of Arithme. tick. The rules are plain, and the demonftrations perfpicuous and fatisfacfingle piece we have and methodical efteem it the best calculated, of any fing tory; met with, to lead youth, by natural and easy gradations, into a we and thorough acquaintance with the science of figures. Perfons of all de-. scriptions may find in it every thing, respecting numbers, neceffary to their business; and not only fo, but if if they have a fpeculative turn, and mathematical taste, may meet with much for their entertainment at a leisure hour. We are happy to fee so useful an American production, which, if it should meet with the encouragement it deserves, among the inhabitants of the United States, will fave much money in the country, which would other wife be sent to Europe, for publications of this kind. We heartily recommend it to schools, and to the community at large, and wish that the industry and skill of the Author may be rewarded, for fo beneficial a work, by meeting with the general approbation and encouragement of the publick. JOSEPH WILLARD, D. D. President of the University. S. WILLIAMS, L. L. D. Math. et Phil. Nat. Prof. Hollis. Yale College, 1786. UPON examining Mr. Pike's System of Arithmetick and Geometry, in manuscript, I find it to be a work of such mathematical ingenuity, that I ef. teem myself honoured in joining with the Rev. President Willard, and other learned gentlemen, in recommending it to the publick as a production of genius, interspersed with originality in this part of learning, and as a book, fuitable to be taught in schools: of utility to the merchant, and well adapted even for the University instruction. I confider it of such merit, as that it will probably gain a very general reception and use throughout the republick of letters. EZRA STILES, Prefident. Boston, 1786. FROM the known character of the Gentlemen who have recommended Mr. Pike's System of Arithmetick, there can be no room to doubt, that it is a valuable performance; and will be, if published, a very useful one. I therefore with him success in its publication. JAMES BOWDOIN. 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 fow, who are conspicuous for their knowledge in the Mathematicks, that the books, now in use among us, are generally 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 beretofore 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 apprebending I 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 siria 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 Roots, and of a particular Theorem for the Sursolid. Among the Miscellaneous Questions, I have given some of a ¡hilosophical 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 businesses of life. The short introdution to Algebra, which is subjoined, was abstracted principally from Bonnycastle, and that of Conick Sections, from Emerson's Works. Being sensible the foliowing 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 correlling, 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 bumble Servant, THE AUTHOR |