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SYSTEM OF ARITHMETICK.

COMPOSED FOR THE

USE OF THE CITIZENS

OF THE

United States.

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
TO THE FEDERAL CURRENCY,

By NATHANIEL LORD, a. m.

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Boston.

PUBLISHED BY THOMAS & ANDREWS,

Proprietors of the Copy-Right. Sold at their Bookstore, No. 45, Newbury-
Street, and by the Booksellers throughout the United States.
APRIL, 1808

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BE it remembered, that on the thirty first day of March, in the thirty fecond 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 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, A. M."

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 fupplementary to An Act, intitled, An Act for the Encouragement of Learning, by fecuring the Copies of Maps, Charts and Books, to the Authors and Proprietors of fuch Copies during the times therein mentioned; and extending the Benefits thereof to the Arts of Defigning, Engraving and Etching Historical and other Prints."

WM. SMITH SHAW, Clerk of the District of Massachusetts

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Dartmouth University, A. D. 1786.

AT the request of Nicolas Pike, Efq. we have infpected his Syftem of
Arithmetick, which we cheerfully recommend to the publick, as eafy, ac-
curate, and complete. And we apprehend there is no treatife of the kind
extant, from which fo great utility may arife to Schools.

B. WOODWARD, Math. and Phil. Prof.
JOHN SMITH, Prof. of the Learned Languages.
I do moft fincerely concur in the preceding recommendation.
J. WHEELOCK, Prefident of the University.

Providence, State of Rhode-Ifland, 1785. WHOEVER may have the perufal of this treatise on Arithmetick may naturally conclude I might have fpared myfelf the trouble of giving it this recommendation, as the work will fpeak more for itfelf 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 fubjects, and at the fame time fully fenfible of the utility of a work of this nature, was willing to render every affiftance in my power to bring it to the publick view : And fhould the ftudent read it with the fame pleafure with which I perused the fheets before they went to the prefs, am perfuaded he will not fail of reaping that benefit from it which he may expect, or wifh for, to fatisty his curiofity in a fubject of this nature. The author, in treating on numbers, has done it with fo much perspicuity and fingular address, that I am convinced the ftudy 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 feen. Wingate, Hatton, Ward, Hill, and many other authors, whofe names might be adduced, if neceffary, have claimed a confiderable fhare 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 ufeful and neceflary 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 exercife of their genius; and am well affured it may be read to great advantage by ftudents of every clafs, from the loweft fchool to the Univerfity. More than this need not be faid by me, and to have faid lefs, would be keeping back a tribute juftly due to the merit of this work.

BENJAMIN WEST.

Univerfity in Cambridge, A. D. 1786. HAVING, by the defire of Nicolas Pike, Efq. infpected the following volume in mannfcript, we beg leave to acquaint the publick, that in our opin ion it is a work well executed, and contains a complete fyftem of Arithme tick. The rules are plain, and the demonftrations perfpicuous and fatisfactory; and we efteem it the beft calculated, of any fingle piece we have met with, to lead youth, by natural and eafy gradations, into a methodical

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and thorough acquaintance with the fcience of figures. Perfons of all de-. fcriptions may find in it every thing, refpecting numbers, neceffary to their bufinefs; and not only fo, but if they have a fpeculative turn, and mathematical tafte, may meet with much for their entertainment at a leisure hour.

We are happy to see so useful an American production, which, if it should meet with the encouragement it deferves, among the inhabitants of the United States, will fave much money in the country, which would otherwife be fent to Europe, for publications of this kind.

We heartily recommend it to fchools, and to the community at large, and wifh 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. Prefident of the University.
E. WIGGLESWORTH, S. T. P. Hollis.

S. WILLIAMS, L. L. D. Math. et Phil. Nat. Prof. Hollis.

Yale College, 1786.

UPON examining Mr. Pike's Syftem of Arithmetick and Geometry, in manufcript, I find it to be a work of fuch mathematical ingenuity, that I ef. teem myself honoured in joining with the Rev. Prefident Willard, and other learned gentlemen, in recommending it to the publick as a production of genius, interfperfed with originality in this part of learning, and as a book, fuitable to be taught in fchools: of utility to the merchant, and well adapted even for the University inftruction. I confider it of fuch merit, as that it will probably gain a very general reception and ufe throughout the republick of letters.

EZRA STILES, Prefident.

Bofton, 1786.

FROM the known character of the Gentlemen who have recommended Mr. Pike's Syftem 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 fuccess in its publication,

JAMES BOWDOIN.

TO THE FIRST EDITION.

IT may, perhaps, by some, be thought needless, when Authors are so mul tiplied, 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 exbausted. 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 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 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 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 Fradions.

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 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 businesses of life.

The short introduction to Algebra, which is subjoined, was abstracted principally from Bonnycastle, and that of Gonick Sections, 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 subscriptions; and to request the reader to excuse any errours he may meet with; for although great pains have been taken in correding, yet it is difficult to prevent errours from creeping into the press, and some may have escaped my odun observation ; in either case, a hint from the candid will much eblige their

Most obedient,

Aud bumble Servant,

THE AUTHOR

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