From Prof. E. A. Andrews.

About two years ago, I had the pleasure of meeting with Mr. Tracy, and of having some conversation with him on the subject of an Arithmetic which he was preparing for schools. I was particularly pleased with that part of his system which related to canceling, and which appeared to me to possess great practical value. Within a few days, Mr. Tracy has put into my hands a part of his manuscript, that I might become more minutely acquainted with his system. My time has been so far occupied with my own business, that I have been able to examine a part only of the manuscript put into my hands; but with this part I have been much gratified. It appears to me, that, when carefully and thoroughly revised and perfected, as the author designs to do, it may become a most valuable work, inferior to none of the Arithmetics now used in our schools. Such is my confidence in the ability of the author to complete and polish the work, that I look upon its success as quite certain.

From E. H. Burritt, Author of the Geography of the Heavens, &c. Through the politeness of Mr. Tracy, I have been favored with a perusal of an Arithmetic, in manuscript, which he is preparing for publication. The work is intended as a universal class-book in elementary arithmetic. It is the production of a gentleman of known abilities and experience in teaching; and he has, with great care, arranged its several parts, and given the rules, and selected the examples, step by step, in that natural order, and easy method, which his own judgment and experience approved. There are some excellences in his Arithmetic, some facilities of dealing with figures, which, so far as I know, are entirely peculiar to this treatise, and which distinguish it from all others. On this ground especially, and that of its general merit, I think it a work which will conmend itself to the attention of teachers.

I entirely coincide in the above opinion, having been particularly gratified with the ease and facility with which many difficult operations are performed by the new principle introduced by the author. J. P. BRACE, Principal of Hartford Female Seminary.

From E. C. Herrick, Esq.

I have cursorily examined the manuscript of Mr. C. Tracy's treatise on Arithmetic. The most prominent feature of the work is the introduction of a peculiar mode of stating numerons classes of problems, which are then solved by an abridged process, called canceling. This appears to me an important improvement on the books in common use, and one which renders the publication of this treatise very desirable.

From La Fayette S. Foster, Esq.

Mr. Calvin Tracy has submitted to my examination, in manuscript, an Arithmetic prepared by himself for publication. From the known ability of Mr. Tracy as an instructor, I was prepared to entertain a high opinion of any treatise designed to facilitate the acquisition of knowledge, of which he might be the author; and from the attention which I have bestowed on his Arithmetic, I have no hesitation in bearing testimony to its high meritorious character. His plan appears to me to be highly judicious, and ably and skillfully executed. The work, in my opinion, will be a valuable addition to a very important branch of education.

Extract of a Letter from J. J. Van Antwerp, Esq., Principal of Coxsackie

Academy, N. Y.

Dear Sir I have heretofore given the preference to "Adams's New Arithmetic," and have always made use of it. I consider yours equally as good, if not superior to it, as far as your system is not "New." Your system of canceling I regard as an important improvement, especially for those pupils who are called "good in figures," and I am not sure but it may help to arouse the stupid and dormant faculties of the dull. We wish to make ready and correct accountants; - your system strikes me as tending directly to such a result.

Extract of a Letter from M. N. Morris, Esq., Principal of Colchester

(Conn.) Academy.

From the defective manner of treating the principle of canceling, so far as I had seen allusions to it in works published previously to yours, I had been led to think unfavorably of it, the method having been merely alluded to, without any clear investigation of the principle itself. Instead of so doing, you have, however, first led the scholar in the plain, obvious course, to the result, and have then taught him to abbreviate the operation, by the application of well-known and obvious principles. The defective manner to which I have alluded, you have therefore avoided. In applying the principle of canceling, as laid down in your book, the student secures even a clears es his subject, than in the ordinary A

mode of solution. I can therefore cheerfully express the opinion, that, although several valuable treatises on arithmetic have appeared within a few years, your work combines excellences which are rarely, if ever, to be found without resorting to different systems. The general perspicuity and conciseness of explanations and illustrations, the complete ness of the work as a system, and the happy application of the principle of canceling, give it strong claims on the attention of those who have the care of educating the young.

From S. Smith, Esq., Principal of Boarding School, Poughkeepsie, N. Y. I have examined a new system of Arithmetic by C. Tracy, Esq., and find it well adapted to the use of schools. The arrangement and mode of treating the subject are more definite and perspicuous, and, in fact, better than are those of any other Arithmetic with which I um acquainted.

From R. S. Howes, Principal of Academy, Troy, N. Y.

I have examined a system of Arithmetic by C. Tracy, Esq., and, as the result, am satisfied that it is superior to any other work with which I am acquainted. The method of canceling introduced must secure success to the work, being, as it is, well calculated to render those who study it quick in figures and prompt in business.

From E. Wilson, Jr., Principal of Monitorial School, Troy, N. Y.

I have recently examined a treatise on Arithmetic by C. Tracy, Esq. Both the matter and manner of the work are judicious, -the former embracing all that the habits of our men of business require; the latter, all the advantages which other systems contain, together with the new and peculiar mode of canceling, which very much abridges the processes of solution. In these particulars, the work is an improvement upon former systems.

From J. H. Rogers, Esq., Principal of Prospect Hill High School. Messrs. DURRIE & PECK,

Gentlemen-From a hasty examination of Tracy's Arithmetic, I believe it worthy of being ranked among the best school books. The method of canceling, very fully brought into practice in this work, greatly abridges many operations, and may be mentioned as J. H. ROGERS. Sincerely yours, one of its most valuable features.

From Rev. A. Bond, Pastor of the Second Congregational Church in Norwich Having examined the general plan of an Arithmetic, prepared by Mr. Tracy, Principal of Norwich Academy, I can cheerfully recommend it as a system possessing, in some important particulars, a superiority over any other system with which I am acquainted. The method of canceling, which is carried through the work, excepting the Roots, greatly facilitates the process of arithmetical calculations, and will give it a decided advantage in the estimation of business men. The part on foreign exchanges will enhance its value with the commercial community. While its simplicity adapts it to the use of common schools, its comprehensiveness, and the ease and accuracy with which complicated problems may be solved, will be likely to secure for it a prominent place in the counting room.

From Rev. L. N. Tracy, formerly Principal of New Britain Academy. I have spent considerable time in a careful examination of an Arithmetic prepared by Mr. C. Tracy, Principal of Norwich Academy. For my own benefit and pleasure, I have carefully examined every rule; and though I have daily used the best Arithmetics extant, while engaged for many years in teaching, I am led to believe that there is not a text-book on arithmetic in use which presents equal excellences. Its grand feature that which distinguishes it from every other arithmetical treatise is the principle of canceling, introduced and applied throughout the work. The extent and facility of its application to all operations in which multiplication and division are both concerned, are fully and clearly lustrated. It is safe to say that two thirds, and often four fifths of the labor and time 1sually required for arithmetical solutions, are saved. While it contains an amount of catter equal to any other Arithmetic in use, it is still a strictly elementary work.

The following is from the Board of Visitors of the First School Society of the wn of New Haven, who are by law appointed to determine what books shall be used in the schools under their superintendence.

The undersigned, Visitors of the First School Society in the town of New Haven, having, by means of a committee of our body, made examination of the "New System of A ithmetic," prepared by Mr. C. Tracy, Principal of Norwich Academy, and considering twork to contain important improvements on the treatises in common use, do hereby di ect the said book to be adopted in the Schools of this Society.

R. S. HINMAN,
ALLING BROWN,
EDWARD C. HERRICK,

NEW HAVEN, April 29, 1840.

R. H. OSBORN,
GEORGE F. SMITH,
WYLLIS PECK,

School Visitors.

A

NEW SYSTEM

OF

ARITHMETIC;

IN WHICH IS EXPLAINED AND APPLIED TO PRACTICAL PURPOSES, IN
ADDITION TO THE ORDINARY RULES OF OPERATION,

Entered according to Act of Congress, in the year 1840, by

DURRIE AND PECK,

In the Clerk's Office of the District Court of Connecticut District.

STEREOTYPED AT THE
BOSTON TYPE AND STEREOTYPE FOUNDRY.

08-9-54 mau

Jolin 12-15-30 23095

INTRODUCTION.

Ir will readily be conceded, that all efforts in behalf of the general diffusion of useful knowledge, are in themselves commendable. There is, however, and probably ever will be, a difference of opinion relative to the extent to which books of any particular description, and treating upon the same general topic, may be multiplied, and the interests of education uniformly advanced thereby.

This difference of opinion exists especially in relation to books designed for the use of common schools and academies, and which treat upon the more common subjects of study. The multiplication of books of this description, to the extent realized at the present day, is regarded by many as injurious to the general good. That its tendency is to increase, in some small degree, the expense of education — at least in some parts of the country-will not be denied. But, before sentence of final condemnation is pronounced, it always becomes those, who sit as umpires, to take as extended views of the subject before them, as the nature of the case will admit.

The question now presented is, how far the general good is advanced by the multiplication of school books.

To answer this, let it be supposed that only a single work in each department of science studied in common schools, had ever been presented to the public, and that each work were such as it should be. Books of this description would obviously find ample circulation, sufficient, perhaps, to satisfy both authors and publishers, without embracing one half of the ground to be occupied. The consequence would be, that the more recently settled parts of our country would be but poorly supplied with the means of education, for at least some considerable period of time. But, as it now is, with such a multiplicity of school books constantly emanating from the press, a spirit of rivalry is created, a desire is excited on the part of both authors and publishers to give to their several works a more extended circulation than can be obtained without exploring the whole ground. As a natural consequence, the inhabitant of the less favored portion of our land is scarcely settled in his log cabin, before books of every description necessary for the education of his sons and daughters, are presented him, as it were, at his own door. His attention is thus directed to a subject second in importance to none of a temporal nature; and one which, when duly presented, will be likely to be regarded, and to receive a consideration, which otherwise might be long neglected.

The truth of our supposition, that any one set of school books is such, in all respects, as is required, may, however, very reasonably be doubted. Many of them are unquestionably of a high order, and probably owe some degree of their merit to the fact, that other minds have been, are, and yet will be, traversing the same ground which their authors trod, and are preparing other works to supersede them, if possible, in the estimation of the public.

The effect of the multiplication of school books is, therefore, to render the means of education as perfect as the nature of their subjects will allow, and to convey these means, thus perfected, to every part of our entire country.

From the preceding considerations, the author is inclined to regard the multiplication of school books as favorable to the cause of general education. It therefore only remains to point out some of the more important

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