Southern District of New-York, ss BE IT REMEMBERED, That on the 14th day of May, A. D. 1828, in the fifty-second year of the Independence of the United States of America, DANIEL PARKER, of the said District, has deposited in this office the title of a Book, the right whereof he claims as author, in the words following, to wit:

"The Improved Arithmetic, newly arranged and clearly illustrated, both thecretically and practically, to meet the exigencies of the Student in the acquisition of the nature and science of numbers; and also to aid the accountant in all arithmetical computations relative to business transactions. Designed for the use of acade mies, schools, and counting-houses. By Daniel Parker, A.M., late Principal of several distinguished literary institutions."

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 to the authors and proprietors of such copies, during the times therein mentioned." And also to an 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 of designing, engraving, and etching historical and other prints."

FRED. J. BETTS,

Clerk of the Southern District of New-York.

키이

P238

1828

2-4-39 Nem.

THE object of the following pages has been to facilitate the acquisition of Arithmetic, by rendering its principles more simple, and easy of comprehension by the student.

In the execution of this object, the design has been to adhere strictly to the order of nature in the arrangement of the several rules-clearly to exhibit the nature, powers, and operations of numbers-the similarity and intimate relations between rules distinguished by different names, but in reality of similar import; and also the why's and wherefore's, generally, that such effects should necessarily result.

The subject of notation and numeration has here received more attention than what has been usual by authors. This has been occasioned from a full conviction, that enough had not been written or exemplified, to furnish the learner with sufficiently clear and adequate ideas to prepare him to enter, with profit, on the subsequent rules. The collocation of decimal notation, and numeration, in connection with that of whole numbers, will be obvious from the consideration, that without some knowledge of the punctuation of decimals, the student would be wholly incompetent to the management of federal money, in the ground rules of Arithmetic.

The rules of increase and decrease, with their respective subdivisions, are newly arranged. The object manifestly is, to render more clear and intelligible to the learner, the nature and similarity of rules which retain entirely different names. In this manner the learner will more obviously discover, that the nature and principles of the rules of addition and multipli

cation must necessarily produce one and the same result; viz. they both inevitably produce an increased quantity; and that the latter rule is only a contracted method of executing the work of the former: in like manner also of decrease, viz. subtraction and division, both lessen or diminish the quantity; and the latter rule is only a contraction of the work of the former

In the change of currencies and the reduction of coins, methods have been adopted, probably in some respects new, yet designed to simplify the labour; and by illustrating the principles of the various changes, to preclude the necessity of burdening the memory with the necessary retention of certain given numbers.

Proportion in general is placed before the rule of three; and the nature of proportion, with the distinctions between arithmetical and geometrical proportions and progressions, is carefully distinguished. This appeared to be indispensably necessary, from the consideration, that the rule of three, and most of the subsequent rules in the system of arithmetic are founded exclusively on the principles of proportion. Hence without any discriminating ideas of these important principles, the student would be left in much perplexity relative to any proper solutions of the nature and principles of all the various rules which have proportion for their basis.

The rules for interest have been pursued farther than is usual, and extended to a great variety of forms, so as to be rendered applicable to all the various business transactions, in which premiums on loans, commissions, &c. &c. require computations. Many rules are given and exemplified, some of which have probably never before been published.

The subject of foreign exchange has been enlarged upon, and the moneys of most of the commercial places on both continents have been given, to aid accountants in the more ready discharge of their labours.

Mensuration, ship's tonage and cask gauging have been appended to the work, for the purpose of embracing, very extensively, the different methods requisite in the various arithmetical calculations, and thereby to render the system of arithmetic the more complete.

The design of the questions placed under the several rules is, that the knowledge of the pupil may be easily tested, in the various rules, as he gradually advances. If, when he has passed over a rule, he can readily answer the questions under it, it is evident he thoroughly understands the nature and import of the rule; and that no seeming labour was required on his part to solve each question: on the contrary, if the questions become irksome to the student, he at once betrays his ignorance of the nature and design of the rule, and requires to be put to the im mediate revision of it.

Brevity has been consulted under each rule, so far as was deemed consistent, and still furnish a clear conception of the nature and principles of each respective rule. It is not the quantity of examples under each rule which is the great desideratum, but the clear elucidation of the rule by explanations, and a few examples, which render the principles of the rule clearly comprehensible by the student.

It appeared necessary also, that the treatise should be full and perspicuous, and at the same time evade, if possible, the imputation of its being too voluminous for a ready and practical elementary work This consideration has operated to neglect the solutions of several rules, as necessarily occupying too much space, together with the consideration, that comparatively. very few regard, with any care or attention, the solutions referred to, viz. those relating to the different roots. Yet should the size not be considered objectionable, and the work merit sufficient patronage, these omissions, possibly, may hereafter be inserted.

The multiplicity of rules and notes of illustration which are given in this work, does not necessarily imply, that the learner must consequently commit the whole to memory. The object is, to elicit ideas in the minds of learners, and to furnish them with clear conceptions of elementary principles, which, when once clearly conceived, they can readily communicate to others, dressed, if requisite, in their own language, yet fully expressive of the true meaning and import of the rules. In this view, there is no task in really committing to memory; for it is not committing simply a phraseology of words to them of no meaning,

but it is the clear reception of the ideas, which are thus clothea with words. Still more absurd is it, that youth should be required to work out examples, without any requisition of the rules, either in their principles or phraseology; for in such a case the examples can have no application, in their estimation, to any supposed rule whatever. Hence their time and labour are lost, and worse than lost, for the want of proper direction and cultivation.

Long experience in the instruction of youth, has clearly evinced the indispensable necessity of early inculcating elementary principles upon the minds of youth. This lays a foundation for the regular growth and enlargement of their mental powers; and such early render themselves distinguished proficients in the various branches of science to which they devote attention.

It was the apparent necessities of the youth which influenced the author to engage in this work. Gladly would he contribute his feeble effort to aid "in the removal of the rubbish, that the skill of the polisher may not only cause the surface to shine," but also exhibit to view "the latent beauties and qualities" of the mind in a more conspicuous manner.

The work, such as it is, is now presented before the public, and submitted to the decisions of the candid, the judicious, and impartial.

New-York, August 1st, 1828.

THE AUTHOR.