DESIGNED FOR THE USE OF HIGH SCHOOLS, ACADEMIES, AND COLLEGES; IN WHICH SOME ENTIRELY NEW PRINCIPLES ARE DEVELOPED, AND MANY BEFORE APPEARED IN ANY ARITHMETIC : WITH AN APPENDIX. By GEORGE R. PERKINS, A. M., PRINCIPAL AND PROFESSOR OF MATHEMATICS OF THE NORMAL SCHOOL OF THE STATE OF TREATISE ON ALGEBRA, ELEMENTS OF GEOMETRY, ETC., ETC. STEREOTYPE EDITION, REVISED AND IMPROVED. NEW YORK: UTICA. 1851. EducT18.51.680 HARVARD COLLEGE LIBRARY GIFT OF THE DEC 11 1935 ENTERED according to Act of Congress, in the year 1848, by GEORGE R. PERKINS, STEREOTYPED BY PRINTED BY HARTFORD, CONN. PREFACE TO THE SECOND EDITION. In preparing this edition, the whole work has been carefully revised, and many of the subjects re-written and modified, with a view to make them more clearly comprehended by the pupil. Having explained fully, in the ELEMENTARY ARITHMETIC, the subjects of Duodecimals and Alligation, we have omitted them in the present edition. We have excluded the chapter on Permutations, Combinations, and Variations, to make room for what we deemed matter of more importance. We have also placed the chapters on the Progressions after Evolution, because severa, cases under the Progressions are wrought by the aid of Evolution. Under the first chapter, we have added some new things concerning Prime Numbers, and have explained the use of ERaTOSTHENES' Sieve in finding these numbers. After Continued Fractions, we have added LAMBERT'S Method of De-compounding Vulgar Fractions. We have given a new rule for the Equation of Payments, under the subject of Discount. This rule is deduced from considering the equivalent present values. By this method, we discover that the usual rule is erroneous, if we consider the present value of the several debts. We have added the answers to all the questions; and, where we thought the operations too difficult, we have either given the whole work, or so much as to leave nothing to perplex the beginner. In all these modifications we have been guided, not only by our own practical experience in using the book, but by the many kind suggestions which have been received from distinguished teachers. GEO. R. PERKINS. UTICA, September, 1844. |