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ess, in the year 1864, by
f the District of Massachusetts.
THIS book is designed to prepare the pupil to meet the demands of actual life. It is itself copious in examples of a great variety of forms, and largely of a practical character; and the accompanying Key contains a set of DICTATION EXERCISES, adapted to every important topic treated in the book, to be used at the discretion of the teacher, by means of which the amount of practice may be increased almost indefinitely.
All that the book contains is written for the pupil; and if he will learn it understandingly, he may master the principles of arithmetic with but little aid from the teacher.
In the arrangement of subjects, that order has been adopted which experience has shown to be the best for all classes of learners. Some subjects, of little importance, have been briefly treated; others have been transferred to the Appendix. Should any subject, as Duodecimals, Circulating Decimals, or Average of Accounts, or any examples prove too difficult for the younger scholar, they can be omitted till the book is reviewed.
Answers are given to the examples, so far as is necessary to assure the pupil that he understands the principles; but every important principle is likewise tested by examples having no answers in the book. The answers not contained in the book may be found in the Key, from which they can easily be transferred to the black-board, if the teacher prefers to have them placed before his pupils.
To determine the adaptation of a text-book to school purposes, it (3)
must be used in the school-room. This treatise has already been successfully tested by this standard, since its general character has been determined by the actual demands of a large grammar school, at present and for several years in the charge of the undersigned, and since it is largely illustrated by examples which have been repeatedly employed to familiarize students with the principles they here exemplify. Its practical character is fully certified by the testimony of many of its students, now business men, who practise its methods in the office and in the counting-room.
Though, at the request of the publishers, but one name appears upon the title-page as author, the book is the joint production of the person whose name it bears, and of E. N. L. WALTON, former teacher in one of the State Normal Schools of Massachusetts; and whatever merits or defects the book may be found to possess, may be attributed equally to each.
Our grateful acknowledgments are due to many teachers and business men for valuable suggestions, particularly to WM. J. ROLFE, A. M., of Cambridge, for important criticisms while the work was in preparation for the press; to FRANCIS COGSWELL, Esq., of Cambridge, for hints on methods of Reviews; and to the teachers of the Oliver Grammar School, Lawrence, for their kind assistance in solving and testing examples.
GEO. A. WALTON.
LAWRENCE, Oct. 1, 1864.
be used in the school-room. This treatise has already been suc
th, at the request of the publishers, but one name appears upon
teful acknowledgments are due to many teachers and business
GEO. A. WALTON.
Reduction to Lowest Terms,
PROPERTIES OF NUMBERS.
64 | To find the Whole from a Part,.
65 What Part one Number is of another, 80
Reduction of Whole and Mixed Num-
Greatest Common Divisor of Frac-
72 Least Common Multiple of Fractions, 88
Average or Equation of Payments, . 215
Custom House Business,
Analysis and Simple Proportion, . . 249
Analysis and Compound Proportion, 254
Divisibility by 9,
Contractions in Multiplication,
.248 Circles, Similar Triangles, Polygons, 293
Methods of Computing Time,.
Table for finding Difference of Days, 331