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Entered according to the Act of Congress, on the 21st of November, in th: year one thousand eight hundred and thirty-one, by WM. S. PARKER & Sox in the Clerk's Office of the District Court of the United States, for th. Northern District of New-York.

The constant demand for this valuable work has induced the Proprietors to incur the expense of presenting it to the public in a more perfect form than heretofore, being printed from beautifully executed Stereo. Plates. It is very desirable that a work of this kind should be as faultless as possible; the publishers will therefore feel grateful to all Preceptors and others who make use of it, to cominunicate to them by letter, all errors that may be discovered by them, that they may be corrected in future editions.

TROY, FEBRUARY 29, 1832.

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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 i of not a few, who are conspicuous for their knowledge in the Mathe

maticks, 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 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 business 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 gratitude to those learned Gentlemen, who have honoured this I'reatise with their approbation, as well as to such Gentlemen, as have encouraged it by their subscriptions; and to request the reader to excuse any errors 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 observation; 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 designed 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 too, 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 copyright, 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. It 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 distiuguished teachers of Arithmetick, are to a great degree remedied in the present edition.

The alterations 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 enlarged. Several simple and obvious rules were redundant and have been omitted. The Rule of Three and Interest have been much improved. Demonstrations 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, Trigonometry, Algebra, and Conic Sections, are omitted. These subjects were so briefly treated by Mr. Pike, as to possess little 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 now publishing 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 its value.

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

THE PUBLISHER. TROY, OCTOBER 31, 1822.

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