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It is a work of an order superior to any that has issued from the American press on the subject, in the highest degree creditable to the professor, and to the science of the country. Indeed, I am acquainted with no work on arithmetic in the English language equal to it. I am confident that its general adoption as a text-book, by our seminaries, would be considered by all who feel an interest in the promotion of the exact sciences, as an omen of good.

In great haste, your ob't serv't, I. W. Jackson.

From B. Birdsall, Professor of Mathematics, Clinton Liberal Institute.
CLINToN, May 28, 1841.
MessRs. BENNETT, BACKUs, & Hawley:
GENTLEMEN-I have examined with considerable attention “Perkins'
Higher Arithmetic,” and am favorably impressed with its excellence.
It has been introduced here as one of the text-books for the use of those
students who have already a knowledge of elementary arithmetic. The
author is very clear in his explanations, systèmatic in the arrangement,
and the examples are numerous and well.selected. In the explanations
which generally precede the rules, the student is carried on by a kind
of inductive process, to a perception of the principle ou which the rule
is founded. The article on continued fractions—which are so useful in
determining approximate ratios—supplies a deficiency which exists in
all other systems of arithmetic with which I am acquainted. In short,
there are many new and interesting properties of numbers exhibited in
the body of the work, which will, I believe, render it acceptable even
to advanced students. The new and concise methods which are given
for the extraction of the cube and other higher roots, will of themselves
sufficiently commend the work to any one who is favorable to the im:
provement of science. B. BiRDsALL.

I concur in the above recommendation of Perkins' Higher Arithmetic, Timothy CLowes, Principal Clinton Liberal Institute.

From O. Root, A. M., Principal of the Syracuse Academy. SYRAcuse, May 26, 1841. MESSRs, BeNNETT, BACKUs, & Hawley: GENTLEMEN–I thank you for the copy of Prof. Perkins' Arithmetic which you had the kindness to send me. My engagements have prevented me from examining the work very minutely, but from what I have read I am satisfied that it will prove highly useful to those students

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who pursue the study of arithmetic beyond our elementary treatises. I noticed several remarkable properties of numbers calculated to excite the curiosity and exercise the ingenuity of the student, and the exposure of a single defective rule which had so long remained uncorrected should entitle the work to the consideration of all teachers and lovers of the exact sciences. I shall commence an advanced class with the work as soon as it can be obtained. Yours, respectfully, O. Roor. From Marcus Catlin, A. M., A. A. S., Professor of Mathematics and Astronomy, Hamilton College. Clinton, May 25, 1841. Messrs. BENNETT, BACKUs, & HAwley: Gentlemen—I have received a copy of Perkins' Higher Arithmetic which you had the kindness to forward to me. I had often expressed my approbation of the plan to the author while he was preparing the manuscript; and now that I have given the work a somewhat thorough examination, I am happy to say not only that my former opinion of its plan is confirmed, but that the plan has been well executed. This work appears to me to supply a deficiency in the series of text-books now in use; and if it would be generally adopted and introduced into our schools, it would undoubtedly tend to elevate the standard of arithmetical learning which is now unfortunately so low. Yours, &c. MARCUs CATLIN. From J. T. Foster, Principal of the High School, Little Falls. Upon a careful comparison of Perkins' Higher Arithmetic with oth. ers, I am prepared to give it a high place among the books which have been published upon the subject of mathematics. It seems admirably calculated to fill the vacancy which has existed between common arithmetic and algebra. In my opinion it is a work of peculiar excellence. The author has developed many new principles, which have never before appeared in any similar work. Had the author done nothing more than correct the rule for finding the “least common multiple of numbers,” that alone would entitle the work to a large share of public patronage. The method of explaining and developing the principles contained in the work is so clear and concise, that any scholar of ordinary abilities will find no difficulty in readily understanding them. During several years' experience in teaching the higher, as well as the ordinary branches of mathematics, I have found a vacancy which I have endeavored to fill up with oral instruction, without any definite system, till some one emu

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lous to confer a public benefit, should supply the desideratum. Although the work is not designed immediately for primary schools, still every teacher should have a copy of it for his own benefit. I should go on to particularize the excellencies of the work, but, after specifying the “explanation of prime numbers,” the rules for discounting bank notes, permutation, &c., I shall leave its merits to its only true tests, of time and use. J. T. Foster.

From Stephen W. Taylor, Professor of Mathematics and Natural Phi. losophy in Hamilton Literary and Theological Seminary. HAMILTON, May 29, 1841. Messrs. BENNETT, BACKUs, & Hawley: GENTLEMEN–As a lover of learning, and a friend to youth, I feel indebted to any man, who takes pains to give to our schools an improved arithmetic. From reviewing “Higher Arithmetic, by Geo. R. Perkins, A. M.,” I am, therefore, happy to find in it, the plan judicious, the principles clearly developed, the introduction of the rules natural and easy, and the enunciation simple and neat. In my opinion, this book, in comparison with most others extant on the same subject, will serve to advance the student, in the indispensable branch of Mathematics. Very respectfully, yours, - STEPHEN W. TAYLoR,

From Alvin Lathrop, A. M., Professor of Mathematics in Pokeepsie Collegiate School, PoREEpsie, June 4, 1841. Messrs. BENNETT, BACKUs, & HAwLEY: GENTLEMEN-I received from you some weeks since a copy of Prof. Perkins' Higher Arithmetic, and have given it sufficient attention to satisfy me that it is a work of much ability; furnishing abundant evidence of having come from a mind much accustomed to arithmetical investigations, and familiar, in no common degree, with the properties and powers of numbers, and their manifold curious applications. I hope the author may find cheering encouragement and reward for his labors in the approbation of the public and in improved methods of instruction, under his guidance, in the higher department of arithmetic ; a branch of education which, as he justly says, lies at the foundation of all excel. lence in mathematical sciences. Very respectfully, ALVIN LATHROP,

A R IT H M ET I C,

DESIGNED FOR THE USE

HIGH SCHOOLS, ACADEMIES, AND COLLEGES;

In WHICH

soME ENTIRELY NEW PRINCIPLES ARE DEVELOPED, AND MANY
ConCISE AND EASY RULES GIVEN, WHICH HAVE NEVER
BEFORE APPEARED IN ANY ARITHMETIC.

By GEO. R. PERKINS, A. M.,

PRINCIPAL, AND PROFESSOR OF MATHEMATICs, UTICA ACADEMY.

PUBLISHED BY

BENNETT, Backus, & Hawley, UTICA ; Gould, NEwMAN, & Saxton,
NEw York; Gould, KENDALL, & LINcoln, Boston ; A. S.
BARNEs & Co., PHILADELPHIA ; H. STANwood
& Co., RochestER.

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in the Clerk’s Office of the Northern District of New York,
in the year 1840.

BENNETT, BACKU8, & HAWLEY,
PRINTERs, PUBLISHERs, Book-selle Rs, etc.,
Franklin Square, Utica, N. Y.

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