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QUID MUNUS REIPUBLICÆ MAJUS MELIUSVE AFFERRE POSSUMUS, QUAM si ju-
VENTUTEM DOCEMUS, ET BENE ERUDIMUS?
TO THE FEDERAL CURRENCY,
!: 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 said district, have deposited 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 reipublicæ 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,
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 such Copies, during the times therein mentioned ;" and also to an Ad intitled, “ An A& supplementary to An Act, intitled, An A& 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 Deligning, Engraving and Etching Historical and other Prints."
WM, SMITH SHAW, Clerkhof the Diftrict of Massachusetts.
Dartmouth University, 1. D. 1786. At the request of Nicolas Pike, Esq. we have inspected bis System of Arithmetick, which we cheerfully recommend to the publick, as easy, accurate, and complete. And we apprehend there is no treatise of the kind extant, from which so great vtility may arise to Schools.
B. WOODWARD, Math. and Phil. Prof.
JOHN SMITH, Prof. of the Learned Languages. I do most sincerely concur in the preceding recommendation.
J. WHEELOCK, President of the University.
Providence, State of Rhode Island, 1985. WHOEVER may have the perusal of this treatise on Arithmetick may naturally conclude I might have spared myself the trouble of giving it this recommendation, as the work will speak more for itself than the moft elaborate recommendation from my pen can fpeak for it: But as I have always been much delighted with the contemplation of mathematical subjects, and at the same 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 same pleature with which I perused the sheets before they went to the press, an persuaded he will not fail of reaping that benefit from it which he may expect, or wish for, to faristy his curiosity in a subject of this nature. The author, in treating on numbers, has done it with so much perfpicuity and singular address, that I am convinced the study thereof will become more a pleasure than a task.
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 treatise, they are inadequate and defective. This volame contains, befides what is useful and necellary in the common affairs of life, a great find for amusement and entertainment. The Mechanick will find in it nuch more than he may have occalion 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.
University in Cambridge, A. D. 1786. HAVING, by the desire of Nicolas Pike, Efq. inspected the following vol. ume in mannfcript, we beg leave to acquaint the publick, that in our opin. ion it is a work well executed, and contains a complete system of Arithime. tick. The rules are plain, and the demonftrations perspicuous and satisfactory; and we eftcem it the best calculated, of any single piece we have met with, to lead youth, by natural and easy gradations, into a sitnodical
and thorough acquaintance with the science of figures. Persons of all de fcriptions may find in it every thing, respecting numbers, necessary to their business; and not only so, but if they have a speculative turn, and mathematical taste, may meet with much for their entertainment at a leisure hour.
We are happy to see so useful an American production, which, if it thould meet with the encouragement it deserves, among the inhabitants of the United States, will save much money in the country, which would otherwise 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 lo beneficial a work, by meeting with the general approbation and encouragement of the publick.
JOSEPH WILLARD, D. D. President of the University.
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, suitable to be taught in schools : of utility to the merchant, and well adapted even for the University instruction. I consider it of such merit, as that it will probably gain a very general reception and use throughout the republick of letters.
EZRA STILES, President.
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 ufeful one. I there. fore with him success in its publication,
TO THE FIRST EDITION.
IT may, perhaps, by some, be thought ncedless, when Authors are so multiplied, to attempt publishing any thing further on Arithmetick, as it
be imagined there can be nothing more than the repetition of a subjed already exbausted. It is however the opinion of not a fiw, who are conspicuous for their knowledge in the Mathemctieks, 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. Art not only so, but as the United States are now an independent nation, it was juulged that a System mighi de calculated more suitable in our meridian, than those here!efore published,
Alibough I had suficient reason to distrust my abilities for so arduous a task, yel nai knowing any one who would take rapon bimself ihe trouble, and apprebending I could not render the publick more essenticil service, than by an 'a:temp! to remove the difficulties complained of, with diffidcnce I devoted myself to the work.
I bave availed myself of the best Authors which could be obtained, but have foll.wed none particularly, *xcept Bunnycastle's Method of Demonstration.
Alihough I have arranged the work in such order as appeared to me the most regular anil 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 opporlunity for study, may require.
The Federal Coin, being purely decimal, most naturally falls in afier Decimal Fradions.
I have given several methods of extrading the Cube Root, and am indebted to a learned frieni, who declines having his name moule publick, for the investigation of iwo very concise Algebraick Theorems for the cxiridion of all Roots, and of a particular Theòrem 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 busiriesses of lifi.
The short introdufion to digeóra, which is subjoined, was absiraded princi. pally from Bonnycastle, and that of Conick Setiions, from Emerson's Works.
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 sul scriptions ; and to request the reader to excuse any errours he may meet with ; for although great pains have been taken in correčling, yet it is difficult to prevent errours from creeping into the press, and some may have escaped my oëun ciscrvation ; in either case, a hint from the candid will much eblige their