A PRACTICAL ARITHMETIC FOR INTERMEDIATE, GRAMMAR, AND COMMON BY EDWARD OLNEY, PROFESSOR OF MATHEMATICS IN THE UNIVERSITY OF NEW YORK: SHELDON AND COMPANY, 8 MURRAY STREET. 1879. PREFACE. MULTIPLICITY of wants and diversity of tastes are characteristics of advanced civilization. The wigwams of a savage tribe are as uniform in their structure as the nests of a species of birds; and in dress the savages are well-nigh as homogeneous as the birds. On the other hand, scarcely two dwellings in an enlightened community are precisely alike; while endless diversity is seen in the costumes of the inhabitants of the same city. So with intellectual demands. The time has gone by when a single Spelling-Book, a single Reader, and a single Arithmetic will be accepted throughout the country. The necessities of schools are varied, and the views and methods of good teachers are not the same. In reference to Arithmetic, for example, we have every variety of view, from that which would make the mere modus operandi the sole aim, to that which confines attention almost exclusively to the study of principles and to ratiocination; assuming that the pupil well grounded in these cannot be greatly deficient in practical operations. It is this diversity of demand that has led to the preparation of this text-book on Arithmetic now offered to the 3 public. While the Author's "ELEMENTS OF ARITHMETIC has, in a very flattering way, met the wants of teachers who desire to make the study of principles especially prominent; there are still many teachers whose views of the philosophy of teaching, or whose circumstances, demand a less theoretical and more characteristically practical treatise. Such teachers will find their wants met by this book. All statements of principles, definitions, and rules are reduced to the most brief and simple language consistent with clearness and accuracy; and all demonstrations, illustrations, and methods of solution are made as explicit, direct, and practical as possible. While the examples are taken, in large part, from the "ELEMENTS," some of the more complicated of the latter have been omitted, and a great number of ordinary practical exercises have been added. As a book of work, it is believed to be richer than any hitherto offered to the public. The Metric System is presented somewhat earlier and somewhat fuller than in the " Elements;" and a special chapter on Mensuration has been added. In fact, the Author has availed himself of the suggestions of many friends, who have examined the "Elements," and have desired a book containing the same freshness of, and practical adaptation of problems, the same thoroughness in the exposition of principles; but have at the same time desired a book which should be somewhat less a development of a method of teaching, and more characteristically a book of work for the pupil. With a view to meeting the practical wants of the schoolroom in our great graded schools, this |