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Williams College, Oct. 2d, 1832. To Mr. Frederick Emerson. Sir, I have received the First and Second Parts of your North American Arithmetic; and am ghly pleased with the plan of the work, and the manner of ts, execution thus far. It unites simplicity with fulness, and will thus be sure to interest the beginner, whilst it furnishes, at he saihe time, an ample guide to the more advanced pupil. Respectfully and truly yours, ALBERT HOPKINS. [Professor of Mathematics and Natural Philosophy in Williamstown College.]

Union College, Schenectady, Feb. 5th, 1833. Mr. F. Emerson. Sir, I have received the First and Second Parts of the North American Arithmetic, and examined tit with pleasure. The relations of numbers are happily illustrat y the relations of sensible objects. This renders the work more entertaining and instructive, especially at that age to which rithmetic is better adapted than many of those studies which for want of a system like this are too often introduced. Here he student will acquire not merely rules to guide his hand, but rinciples to enlighten his understanding. He is not furnished with a mere mill for grinding numbers into a certain result ader cover Wishing you continued success,

I am, sir, respectfully, your ob't ser't, B. F. JOSLIN [Professor of Mathematics and Natural Philosophy in Union College.]

Burlington, 15th February, 1833. [Conclusion of a Letter to the thor. I should think it hardly cesible that a child could be ally conducted through these No work, bir sad Seered Purtle without being vastly better painted with the subject tu duldren formerly were. Being diciously cor pell. tin son. ensure to invent their own rules, ev can scarcely faleing able to assign a proper reason for e process, as well as to recollect it for future use. Indeed, I o not know any one particular in which, for the use of very oung pupils, they could be improved. Yours respectfully, JAMES DEAN. [Professor of Mathematics and Natural Philosophy, in the University of Vermont.]

Athens, Ohio, February the 1st, 1833. Mr. Emerson. Dear Sir, I have carefully and attentively xamined the "First and Second Parts" of "The North Amer an Arithmetic ;" and can say, with pleasure, that the work eets my cordial approbation You have, perhaps, rendered rithmetic as highly interesting to the youthful mind as the ature of the subject will admit. Your method of illustrating e fundamental principles of Fractions is clear, forcible, and culiarly happy in its adaptation to the minds of youth.

I am, yours, &c. WILLIAM WALL. [Professor of Mathematics, in the Ohio University

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