From La Fayette S. Foster, Esq. Mr. Calvin Tracy, of this city, 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. Norwich, Dec. 24th, 1839. From Messrs. J. H. Gallup and G. Bushnel, Teachers of the Eclectic School, Norwich, Conn. Having examined Mr. Tracy's system of Arithmetic, we think it well calculated to answer the purposes for which it is intended. Mr. Tracy has illustrated, and happily combined with nearly all his operations, a method of abbreviating Arithmetical calculations, which, so far as we know, has never before been published in any common school Arithmetic. This we deem an essential improvement, and are of opinion, that the author has rendered, in this work, an essential service to the cause of education. Norwich City, Oct. 22d, 1839. 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 excellencies. Its grand featurethat 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 illustrated. It is safe to say that two thirds, and often four fifths of the labor and time usually required for arithmetical solutions, is saved. While it contains an amount of matter equal to any other Arithmetic in use, it is still a strictly elementary work. Norwich, Oct. 12th, 1839. 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 numerous 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. New Haven, Dec. 27th, 1839. 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 one of its most valuable features. East Haven, April 24th, 1840. Sincerely yours, J. H. ROGERS. At a meeting of School Visitors of the First School Society of New Haven, held May 2, 1810 The committee appointed at the previous meeting to examine and report on "A New System of Arithmetic," by Mr. C. Tracy,-reported, that in their opinion the work contains important improvements on the arithmetical treatises in common use, and recommend that it be introduced into the schools of this Society:-whereupon, it was Voted, That Tracy's New System of Arithmetic be adopted for use in the schools of the First School Society of New Haven. E. C. HERRICK, Clerk pro tempore. R. S. HINMAN, Chairman. NEW SYSTEM OF ARITHMETIC, IN WHICH IS EXPLAINED AND APPLIED TO PRACTICAL PURPOSES, IN ADDITION PUBLISHED BY DURRIE & PEC K. NEW YORK: COLLINS, KEESE, & CO. 1840. ENTERED, According to Act of Congress, in the year 1840, by DURRIE & PECK, In the Clerk's Office of the District Court of Connecticut District. HITCHCOCK AND STAFFORD, PRINTERS, 9-15-50 APL INTRODUCTION. It 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 very high order, and very 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 features of the following work, before introducing it to the ordeal of public opinion. That it is worthy of public attention and patronage, belongs not to him to decide. It certainly will be found to possess some peculiarities, which are of course regarded by him as improvements. Whether they are indeed such, remains for others to determine. A peculiar feature of the following pages, and one which distinguishes this work from every other on the same subject, is the " System of Canceling," which, in connection with the ordinary mode of solution, is introduced throughout, and applied to such arithmetical problems as embrace in their operation both multiplication and divis ion. This is regarded by the author, and by many others acquainted with his system, as a decided improvement upon all Arithmetics heretofore presented to the public. The following are some of the advantages of the new system: 1st. The statement required, or, rather, recommended for canceling, is itself a complete analysis of the sum proposed. Suppose, for illustration, that 12 yards of cloth cost $48, and that it is required to find the value of 15 yards of the same. = We analyze the preceding sum, either by first finding the value of one yard of the cloth, viz. $48÷12 yd. $4, and then multiplying that price by the number of yards, as, $4X15 yd.- $60, Ans.; or by finding the ratio of the number of yards of which the price is given, and of those of which the price is required, and then multiplying that ratio by the given cost. This ratio is 15 =; and 4×48=60, the number of dollars required, and the same as above. The same stated for canceling: 48. 15 5 5 (See rule for canceling, in Single Proportion.) By the above statement, $48 is to be increased by the ratio, 12:15; or 11⁄2= 2. It is, however, obvious that of 48 multiplied by 15, is the same as 15 multiplied by 48. The above sum is therefore canceled and solved thus: of |