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NORTHERN DİSTRICT 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 tħis 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.”

În 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 oi Designing, Engraving and Etching historical and other prints.”

RICHARD R. LANSING,
Clerk of the Northern Distriel of New York.

TO THE FIRST EDITION.

It may, perhaps, by some, be thought needless, when Authors are so multiplied, to attempt publishing anything further on Arithmetick, as it may be imagined there can be nothing more shan 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 bimself the trouble, and apprehending 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 soch 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 Theoretas for the extraction of all koots, and of a particular Theorem for the Sursolid.

Among the Miscellaneous Questions, I have given some of a phiJosophical nalure, 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 judginent of the candid.

With pleasure I embrace this opportunity, to express my grati. tude 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 heen taken in correcting, yet it is difficult to prevent errours from creeping into the press, and some may have escaped my own observalion; in either case, a hint from the candid will much oblige their

Most obedient,
And humble Servant,

THE AUTHOR

TO THE FOURTH EDITION.

Pike's ARITHMETICK is universally acknowledged to be the most complete system ever published in the United States. It early obtained a very high reputation, and has continued to receive the approbation of the publick, wherever it has been used. It is de. signed for the instruction of our youth in academies and higher schools, as well as for the use of the man of business and the gentleman. All those rules, which are so frequently employed in the various departments of business, are introduced into it. It is the source ton, from which the later Arithmeticks have chiefly been compiled. By them, however, it has not been superseded, so much more full and extensive are its rules and their application. In the deinonstration and illustration of the rules, it stands preeminent.

The continued demand for the work has induced the publisher and proprietor of the copy right, to present to the publick a new and improved edition. In the revision of the work much labour has been bestowed, and in the language of a Mathematician well acquainted with the work, “ to excellent purpose. li is still Pike's Arithmetick, but altogether more perfect than it was before. As a complele system, it may be pronounced superior to any ever published.” The inperfections of the previous editions, which have been noticed by the most distinguished teachers of Arithmetick, are to a great degree remedied in the present edition.

The allerations and improvements consist in the following particulars. Several rules have been added, as well as a variety of Tables, of much practical importance. Some Tables have been corrected and others have been evlarged, Several simple and obvious roles were redunılant and have been omitted. The Rule of Three and Interest have been much improved, Demousira. tions of a large proportion of the rules were not given by Mr. Pike : where the subject would readily admit, they have been supplied. The illustrations of the hules are more copious, and in inany cases simplifier. Most of the Algebraick demonstrations, which are useless to the mere student in Arithmetick, have been exchanged for arithmetical illustrations. Logarithms, Trigonomne. try, Algebra, and Conic Sections, are oinilled. These subjects were so briefly treated by Mr. Pike, as to possess litile value. As they require a large volume of themselves, and are very fully treated of in Day's Course of Mathematicks, and in the system of Mathematicks pow publishing at the University in Massachusetls , ibe publisher has been uniformly advised to omit thein entirely.

A concise System of Book Keeping by single and double Entry has been added to the work, which we besilate not to say will greal. iy enhance its value.

It is confidently believed that this edition will merit the approhalion of the publick, and receive that patronage which has been so liberaliy bestowed on the previous editijns.

THE PUBLISHER. Troy, OCTOBER 31, 1822.

RECOMMENDATIONS.

DARTMOUTH UNIVERSITY, 1786. Ar the request of Nicolas Pike, Esq. we have inspected his 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 utility 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, RHODE ISLAND, 1785. 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 most elaborate reoommendation from my pen can speak 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 pleasure with which I perused the sheets before they went to the press, am, persuaded he will not fail of reaping that benefit from it which he may expect, or wish for, to satisfy his curiosity in a subjuct of this nature. The author, in treating on numbers, has done it with so much perspicu. ity 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 lcads the tyro into the firet 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 considerable share of merit; but when brought into a comparative point of view with this treatise, they are inadequate and defective. This volume contains, besides what is useful and necessary in the common affairs of life, a great fund for amusement and entertainment. The Mechanick will find in it much more than he may have occasion for ; the Lawyer, Merchant and Mathematician, will find an ample field for the exercise of their genius ; and I am weli 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 said by me, and to have said less, would be keeping back a tribute justly due to the merit of this work.

BENJAMIN WEST.

UNIVERSITY IN CAMBRIDGE, 1796. HAVING, by the desire of Nicolas Pike, Esq. inspected the following volume in manuscript, we beg leave to acquaint the publick, that in our opinioa it is a work well executed, and contains a complete system of Arithmetick. The rules are plain, and the demonstrations perspicuous and satisfactory ; and we es. teem it the best calculated, of any single piece we have met with, to lead youth, by natural and easy gradations, into a methodical and thorough acquaintance with the science of figures. Persons of all descriptions may find in it every thing, respecting numbers, necessary to their business; and not only so, but if they have a speculative turn, and matheniatical taste, may meet with much for their entertaiment at a leisure hour,

We are happy to see so useful an American production, which, if it should meet with the encouragement it deserves, among the inhabitants of the United States, will save muci 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 so beneficial a works, by meeting with the general approbation and encouragement of the publick.

JOSEPH WILLARD, 'D. D. President of the University.
E. WIGGLES WORTH, S. T. P. Hollis.
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 esteem 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 in| struction. 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 useful one. I therefore wish him success in its publication.

JAMES BOWDOIN.

UNION COLLEGE, OCT. 10, 1822. PIKE's ARITHMETICK is too well known and too highly appreciated to require any recommendation; and by furnishing an edition of that work, in which common language is substituted for algebraic signs, Professor Dewey has conferred a favour on those who may wish to acquire or teach Arithmetick withou Algebra; by whom it is presumed this edition will be patronised.

E. NOTT, President.

SCHENECTADY, OCT. 16, 1822. Mr. WM. S. PARKER, 1 Hare for many years been fully acquainted with Pike's System of ArithmeTick, and am persuaded of its exceilence ; I do not know of any treatise of more practical utility ; the arrangements of its parts is natural, its rules are plain and casily understood and applied, and it contains all that is of any importance to the Mercantile or Scientific Arithmetician. To those who have not the elementary knowledge of Algebra, the translation of the Algebraic expression into plain Arithmetical language must be very acceptable and profitable. This improveinent, together with the notes and emendations of Professor Dewey, cannot fail to ensure the public confidence and patronage. A hand so able as his, cannot touch without improving an clementary treatise and wherever he is known, his uume must be a sufficient credential.

Wishing you all snccess, and abundant remuneration for your labours, I am, Sir, your friend and servant.

T. MAULEY, S. T. D.
Late Professor of Mathematicks, Union College.

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