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NEW AND COMPLETE
SYSTEM OF ARITHMETICK.
FOR THE USE OF THE CITIZENS
BY NICOLAS PIKE, A.M. A. A. S.
SJID MUNDI REIPUBLICÆ MAJUS MELIUSVE AFFERRE POSSUMUS, QUAM SI
JUVENTUTEM DOCEMUS, ET BENE ERUDIMUS?
REVISED, CORRECTED, AND IMPROVED,
BY CHESTER DEWEY, A.A.S.
PROFESSOR OF MATHEMATICKS, AND NATURAL PHILOSOPHY IY
TROY, N. Y.
PRINTED AND PUBLISHED BY WM. S. PARKER,
SOLD AT THE TROY BOOKSTORE, AND BY THE PRINCIPAL BOOKSELLERS IN
THE UNITED STATES,
VORTHERN 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 Arithmelick, composed for the use of the citi. zens of the United States. By Nicjoßas PIKE, A. M. A. A. S. Quid munus reipublicæ majus meliusve afferre possumus, quam si juventutem docemus, et bene érudimus? E variis sumendum est optimum.-Cicero. Fourth Edition ; revised, corrected, and improved, by CHESTER DEWEY, A. A. 3. 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 entitle! 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 time therein mentioned,' and extending the benefits thereof to the arts of Designing, Engraving and Etching historical and other prints.”
RICHARD R. LÄNSING,
TO THE FIRST EDITION.
It may, perhaps, by some, be thought needless, when Auibors are so multiplied, to attempt publishing any:hing further on Arithmetick, as it may be imagined ihere 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 anlong us, are gen. erally deficient in the illustration and application of the roles; of the truth of which, the general complaint among Schoolmasters is a strong confirmation. And not only so, but as the United States are dow 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 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 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 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 bosioess 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 grali. 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 been taken in correcting, yet it is difficult to prevent errours from creeping into the press, and some may have escaped my own observalion ; in cither case, a hint from the candid will much oblige their
TO THE FOURTH EDITION.
PIKE's ARITAMETICK 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 designed for the instruction of our youth in academies and higher schools, as well as for the use of the man of busjoess and the geotlemaa. 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 demonstration and illustration of the rules, it stands pre, eminent.
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. To the revision of the work much labour has been bestowed, and in the language of a Mathematician well acquainted with the work, "to excelient purpose. li is still Pike's Arithmetick, but altogether more perfect than it was before. As a complete system, it may be pronounced superior to any ever published.” The imperfections of the previous editions, which have been noticed by the most distinguished teachers of Arithme. tick, are to a great degree remedied in the present edition.
The alterations and improvements consist in the following par: ticulars. 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 eolarged. Several simple and obvious rules were redundant and have been omitted. The Rule of Three and Interest have been much improved. Demonstra. 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 Rules are more copious, and in many cases simplified. Most of the Algebraick demonstrations, which are useless to the mere student in Arithmetick, have been exchanged for arithmetical illustrations. Logarithms, Trigonome. try, Algebra, and Conic Sections, are omitted.
These subjects were so briefly treated by Mr. Pike, as to possess little value. As they require a largo volume of themselves, and are very fully treated of in Day's Course of Mathematicks, and in the system of Diathematicks now publishiog at the University in Massachusetts, the publisher has been uniformly advised to omit them entirely.
A concise System of Book Keeping by single and double Entry, has been added to the work, which, we hesitate not to say, will greatly enhance ils yale.
It is confidently believed that this edition will merit the approbation of the publick, and receive that patronage which has been so liberaliy bestowed on the previous editions.
TIIE PUBLISHER. Troy, October 31, 1822.
DARTMOUTH UNIVERSITY, 1786. At 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 recommendation from my pen can speak for it: But as I have always been mucha delighted with the contemplation of mathematical subjects, and at the same time fully sensible of the utility of a work of this nature, I 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, I 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 subject of this nature. The author, in treating on uumbers, has done it with so much perspicuity 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, Hutton, Ward, Hill, and many other authors whose names might be adduced, if necessary, have claimed a considerable share of mer. it ; 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 en. tertainment. 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 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 said by me, and to have said less, would be keeping back a tribute justly due to the merit of this work,
UNIVERSITY IN CAMBRIDGE, 1780. Having, by the desire of Nicolas Pike, Esq. inspected the following volume in manuscript, we beg leave to acquaint the publick, that in our opinion 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 ezteem 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 mathematical taste, may meet with much for their entertainment at a leisure hour.