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self had much experience in the business of instruction, and has thus had occasion ta know where there was room for improvement in the elementary treatises in common use. Without such experience, no one can be qualified to prepare a class-book for schools.-4. D. Stanley, A M., Prof of Mathematics, Yale College.

"I am particularly pleased with the practical character of your Practical Arithmetic, the kystematic and natural arrangements of its parts, the exactness of the definitions, the Clearness with which the principles are explained and illustritted, and the concise, yet ex. plicit language with which the rules are stated. You have done a good service by removing from the tables of Weights and Measures all denominations out of use, and by introducing those adopted by the General Government. The work, in fine, is well adapted to the purposcs of instruction"--Samuel Green, A.M., Principal of the Philips' Grammar School, Boslun, Mass.

" New York, June, 1847. “ 'The undersigned, Commissioners and Inspectors of Common Schools of the Thirteenth Ward, take great pleasure in stating that after a careful and prolonged examination into the relative merits of a great number of Arithmetics, presented for their consid. eration, (which numier embrace all the most popular ones in present use,) have unani, mously adopled Day and Thomson's Mental, and Practical Arithmetics for use in Ward School, No 19., recently organized and opened under their supervision. These books being considered for perspicuity of arrangement, and adaptation to the conaprehension of the pupil, with, or in the absence of a teacher, preferable to any books on the same subject which have come under their consideration."-William A. Walters, William Tyler

Anderson, Charles D. Field. (One vacancy in the Board.) NO. 3.-KEY TO PRACTICAL ARITHMETIC

Containing the Answers to all the Examples ; with many suggestions, and the solu tion of the most difficult questions. 12mo. 38 cents.

The Mental Arithmetic has been published about a year, and the Practical Arith metic about a year and a half. They have been arlopted by the State of Rhode Island Ontario, Livingston, Onondaga, Greene, and Oswego counties, Ņ. Y.; the City of New Haven, Connecticut; Springfield, Mass ; Buttalo, N. Y., and a large number of Acade mies and Schools. No school books have given more entire satisfaction than these Arith

metics. Their success, it is believed, has been unparalleled. NO. 4.HIGHER ARITHMETIC,

Or the Theory and Application of Numbers, combining the Analytic and Synthetic modes of Instruction, adapted to Scientific and Commercial purposes. By JAMES B. THOMSON, A.M. Large 12mno, full bound in leather. 75 cents. Just published

This work is complete in itself, commencing with the fundamental rules, and extending to the highest department of the Science. It is constructed on the principle, that in Aritlimetic, “there is a place for everything, and that every thing should be in its proper place ;" that there is a reason for every operation, and the learner should understand it. It is designed for advanced classes in Schools and Academies, who are preparing for the important office of Teaching, or extended

mercantile pursuits. NO. 5,--KEY TO THE HIGHER ARITHMETIC:

Containing the Answers to all the Examples, with many suggestions, &o NO. 6,--ELEMENTS OF ALGEBRA,

Being a School Edition of Day's Large Algebra. 75 cents. (Durrie & Peck.)

This work is designed to be an easy and lucid transition from the study of Arithmetio to the higher branches of Mathematics. It is highly recommended by Prof. Olmsted, and the Faculty of Yale College ; also by Bishop Potter, Presidents Nott, Wayland, Hopkins

North, and others.

Containing all the Answers, with numerous suggestions. 75 cents. (Durrie & Pock.) VO. 8,--ELEMENTS OF GEOMETRY,

Being an Abridgement of Legendre's Geometry, with Practical Notes and Illustra. tions. Bound in leather. 75 cents. (Durrie & Peck.)

This work has received the warmest approbation of many of the most eminent Teach ers and practical Educators. NO. 9.--ELEMENTS OF TRIGONOMETRY, MENSURATION, AND

LOGARITHMS. NO. 10,--ELEMENTS OF SURVEYING; Adapted both to the wants of the Learner and the Practical Surveyor (Pub. Boon. )



On the subject of the Merits of these works, the publishers will say nothing, bol merely submit the following reasons in favor of their adoption-condensed from the expressed opinions of teachers, superintendents, and committees, who have examiner them.

1.-MENTAL ARITHMETIC. Among the numorous reasong given for the adoption of this work are the following .1. “That it begins and ends in just the right places and in just the right way.”

2. " That it equally avoids the childishness and puerility of some works on the sub fect, and the complication and difficulty of others."

3. “ That th's lessous gradually increase in difficulty, and in a mannor happily adapted to the expanding minds of children, from six to ten years of age.”

4. “ That these lessons are rendered interesting to the young, by the great variety of persons, incidents and circumstances embodied in them-strikingly contrasting with that repulsive monotony, where the same name and the same object occur throughout a whole lesson."

5. “That pictures and marks are excluded from the book, and their places supplied by the Numerical Frame, for the use of which ample instructions are given."

6. “ That the lessons are so arranged that the regular increase of numbers is continually broken up, and thus the solution of each question requires thought and furDishes direct mental exercise for the pupil.”

7. “That in the progress of the book, the first oxample involving a new principle is carefully analyzed, and affords a model of reasoning for the solution of all similar questions."

8. " That after the pupil has become practically acquainted with the principles of a rule, and is able to solve oxamples under it with facility, the operation is then defineda and its more prominent terms briefly explained."

11.-PRACTICAL ARITHMETIC. Among the reasons given for preferring this work we select the following: 1. “That the arrangement of the subjects is consecutive, systematic, and natural.”

2. “That the language omployed in the definitions and rules is peculiarly appropriate, concise, and clear."

3. “That great care is taken never to anticipate a principle, and that no principle is used in the explanation of another, until it has itself been explained or demonstrated.".

4. “That each principle is explained separately, and carefully analyzed-the why and the wherefore of each step in the process are clearly and explicitly given.”

5. “ That the examples are numerous and diversified; their arrangement is gradual and progressive; and the work is calculated to impress upon the pupil's mind an abiding knowledge of the subject.”

6. “That the notes, observations, and suggestions, contained in the work, form an admirable system of instruction for the student, and afford important aid to the teacher."

7. “That Mental Arithmetic, instead of being pursued to a tedious and unprofitable length independent of written Arithmetic, is here immediately connected with it, and is made introductory to every department of the subject. Thus mental operations are connected with the use of the slate throughout the course."

8. “That it is strictly an AMERICAN Book*-arranged in exact accordance with the existing state and national laws, and the practice of business men.”

9. “That the old, obsolete and useless forms of arithmetical operations are rojoctode and their places supplied by valuable improvements."

10. “ That instead of giving the pupil a rule and requiring him to understand it be fore he is furnished with an example, this work first gives an example, then tells the pupil how to do it, and why he did it, and then gives & short, clear and comprehensive rule for it."

11. “ That in nearly every article, something is gained in the mode of presenting the subject, perspicuity and precision being remarkable throughout.”.

12. “That in studying this book, the pupil's mind is thoroughly and actively exer cised; not in seeking for hours to comprehend the meaning of obscure and knotty propositions—the unraveling of which has no more practical bearing than the solution of å riddle or conundrum, but is exercised upon practical and useful principles, which he can understand and apply us occasions for their use arise in after life.”

* Thomson's Practical Arithmetic has the honor of being the first school book which published the standard

units of Weights and Measures adopted by the Government of be United States,



III.-HIGHER ARITHMETIC. $ Among the various reasons given for the adoption of this work, we present the follow ing:

1. “The work is COMPLETE in itself, embracing the fundamental principles of Arith. metic, together with the highest combinations of numbers."

2. “The mode of analysis and reasoning, so successfully pursued in the Mental and Practicad Arithmotics, is admirably carried out in the Higher, and applied to the more Intricate departments of the science."

3. “It is formed upon the plan that there is an intelligible reason for every operation, and that that reason can and ought to be explained to pupils.”

4. “ Nothing has been taken for granted which requires proof."

5. " It happily unites the Philosophy of Arithmetic with its various applications to the practical purposes of life.”

6. “ The rules are arranged in strict accordance with reason and the natural order of the science."

7. “No subject is anticipated, and no principle is used in the explanation of an other, until it has itself been explained or demonstrated.

8. “The principles embraced under each rule are arranged consecutively and sys tematically ; the dependence of each on those that precede it, is pointed out by refer ences-thus presenting a regular and karmonious series of principles and propositions, the study of which must necessarily exert the happiest influence in dorcioping and strengthening the reasoning powers of the learner."

9. “The definitions and rules are remarkably clear, comprehensive, and exact.”

10. “Instead of presenting the rules as mere arbitrary propositions, or inferring them from principles unerplained to the pupil, they are deduced from a careful analysis of examples, and a logical course of reasonıng upon principles already established, the steps of which are plain and intelligible to every youth of common understanding."

11. “ It contains much valuable information respecting business transactions, and matters of science, not found in other works of the kind.”

12. “ It contains the fullest and most satisfactory account of the origin and present standard onlue of American and Foreign Weights and Measures and Moneys of Account of any Arithmetic extant."

The following are some of the Recommendations which the Publishers have received of Day and Thomson's Series. Many others have been received from distinguished practi cal Teachers and friends of education; but our present limits will not admit of their insertion. Its circulation during the brief period since its publication, is believed to be without a parallel, and affords the best practical evidence of its merits :

From Hon. İRA MAYHEW, Sup't of Public Instruction, State of Michigan. GENTLEMEN — Thomson's Higher Arithmetic,” (which you obligingly forwarded me a short time since,) was duly received, and has been critically examined. Having previously examined “ Thomson's Mental and Practical Arithmetics," with much care, and with an unusual degree of satisfaction, I looked for a superior work in the " Higher Arithmetic;" and I am happy (in being able) to say to you, my expectations have been more than realized.

For the last thirteen years I have given special attention to the subject of Arithmeti -in the school-room and in the study-with reference to supplying (or seeing supplied deficiencies in existing works, and obtaining a series adapted to the wants of students of all gradesma series SCIENTIFIC in THEORY, and PRACTICAL in its APPLICATIONS.

In the prosecution of this investigation, I have accumulated a large number of Arith metics. After the most careful examination, I am fully satisfied that each volume in the Bories under consideration is unrivaled. Taken together, as a WHOLE-leading the learner on step by step, from the simplest combinations of numbers through the higher departments of the science-I regard DAY AND THOMSON'S SERIES OF ARITHMETICS THE BEST I HAVE EVER SEEN. I shall recommend their introduction into tho Schools of this state. I trust they will go into general use.

Respectfully yours,




From the Principals of the Albany Public Schools. Within the last few years no less than ten different systems of Art s.etic have boor more or less used in our Schools. About two years since, in view viis evil, we ex aminad several of the more prominent Arithmetics, and agreed with oct unanimity upon Thomson's Series as the best adapted to the wants of the pupi, wr.d the general purposes of instruction.

We are happy to say that, after a trial of more than two years, we die confirmed as to the excellency of tho books, that they have grown in favor by daily use, and that we have succeeded in making better arithmeticians than by the use of any other cas SAMUEL STEELE,





ALBANY, April 20th, 1850.

Fron Hon. Judge Blackman, A.M., Chairman of the Board of School Wie srs of the

City of New Haven, Ct. JANES B. TUOmson, Esq.-Dear Sir:-I have exanined with attention yorr“ Practical Arithmetic," and consider it decidedly the best work for inculcating and illustrating the principles and practice of Arithmetic which I have ever seen. Your illustrations, in the forin of problems to be solvedl, are drawin, in a great measure, from the familiar scenes of early lite; and while the young learner is interested in the solution of probleins which he feels are practicable, he is encouraged to persevero in a study which would other. wise bo dull and forbidding, and is thus imperceptibly led to acquire and understand tho rules of Arithinetic, which he now knows to be true.

I reinaill, dear sir, very respectfully yours,

'ALFREĎ BLACKMAN. At a meeting of the Board of School Visitors of the First School Society of the city of New Haven, Ct., duly warned and convened-

Voted, That the “ Practical Arithinotic,” by James B. Thomson, 1.9., be prescribed for use in each school of this suciety.

ALFRED BLACKMAN, Chairman, Certified by H. G. Lewis, Secretary.

From S. S. Green, A.M., Principal of Philips' Grammar School, Boston, Mass. MR. THOMSON.--Dear Sir:- I hereby acknowledge the receipt of a copy of the “ Practical Arithmetic," to which I have given sufficient attention to be convinced that it possesses superior merit as a text-book. I am particularly pleased with the practical character of it, the systematic and natural arrangement of its paris, tho eractness of the definitions, tho clearness with which the principles are explained and illustrated, and the concise, yet explicit language, with which the rules are stated. You have dono a good service by removing from the tables of weights and measures all denominations out of use, and by introducing those adopted by the General Government. The work, in fine, is well adapted to the purposes of instruction. SAMUEL S. GREEN.

From Rev. C. Pierce, A.M., Principal of West Neroton State Normal School, Mask.

To Mark H. NEWMAN, Esq.-Dear Sir:-The copy of “ Thomson's Higher Arithmetic, which you put into my hands, I have examined with considerable care. Mr. T. he given ui, if not the best, one of the best, school-books which have appeared in this do partment. Besides happily setting forth and explaining the common principles of numbors and their applicating, illustrating the same by appropriate examples both abstract and practical, his book contains many suggestions, in regard to the nature of numbers and inodes of operation, which are ingenious and useful.


From Rev. J. D. Tickham, Principal of Burr Seminary, Manchester, Vt. Having exanined, with some care, the Practical Arithmetic and the Higher Arithmetis of Day and Thomson's Mathematical Series, we know of no Arithmetical treatises that eppoar so well adapted to meet the wants of our Common Schools and Academias. With this belief, we purpose to adopt them for use hereafter in the Burr Seminary.


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