ADVANCED ARITHMETIC FOR HIGH SCHOOLS, NORMAL SCHOOLS AND ACADEMIES BY G. A. WENTWORTH, A.M. AUTHOR OF A SERIES OF TEXT-BOOKS IN MATHEMATICS BOSTON, U.S.A. The Athenæum Press HARVARD COLLIGE LIBRARY GIFT OF MISS ELLEN L. WENTWORTH MAY 1939 COPYRIGHT, 1898, BY ALL RIGHTS RESERVED PREFACE. EVERY high school, normal school, and academy should allow sufficient time for a thorough review of Arithmetic. This book has been written as a text-book for that purpose, and for that purpose only. It is not intended for beginners, but assumes that pupils have previously read a more elementary Arithmetic. The shortest and surest road to a knowledge of Arithmetic is by solving problems. This work is abundantly supplied with well-graded, practical problems, many taken from Wentworth and Hill's High School Arithmetic, but many of them are new, and of a kind to meet the requirements of the present time. These problems are designed to convey a great amount of useful information, as well as to furnish the very best mental training, the primary object of the study. They cover to a great extent the field of mercantile transactions, and so far as practicable the field of science. It is not necessary for any pupil, or any class even, to do all the problems. Every teacher can select such chapters and such parts of chapters as are suited to the needs of his pupils. Decimals are introduced at the beginning of the book. Numbers on each side of the decimal point perform precisely the same office. The only difference is that numbers at the left of the decimal point count whole units, and numbers at the right count equal parts of the unit. Pupils learn the notation on both sides of the decimal point as easily as on one side, provided they have a clear conception of the units counted. Dimes and cents are good examples of tenths and hundredths of a dollar; but decimeters, centimeters, and millimeters, marked on a meter stick, are the best examples of tenths, hundredths, and thousandths of a unit, in general. The Metric System is taught naturally in connection with decimals, and is easily learned. Only the units employed furnish any difficulty. The great number of problems given under the Metric System is to familiarize the learner with the units of the system, to show the simplicity of the system in its application to everyday problems, and at the same time to give practice in operations involving decimals. This system is used in the laboratories of science, and in international transactions. Though not yet adopted by the United States in the common affairs of life, it has certainly forced its way to a position requiring recognition in all secondary schools of the country. The introduction of logarithms into the High School Arithmetic was warmly welcomed by progressive teachers; and the chapter on that subject in this book has been written with special reference to acquiring easily the practical use of a four-place table. Every effort has been made to avoid errors in problems and answers. The author will be very grateful to any one who will call his attention to any mistake that may be discovered. EXETER, N. H., June, 1898. G. A. WENTWORTH. |