JOSEPH RAY, M. D., LATE PROFESSOR OF MATHEMATICS IN WOODWARD INSTITUTION. CINCINNATI: SARGENT, WILSON & HINKLE. CHICAGO: COBB, PRITCHARD & CO. EACH BOOK COMPLETE IN ITSELF, AND SOLD SEPARATELY, Ray's Primary Arithmetic. Ray's Key to Practical Arithmetic. Ray's Test Examples, without Answers. Ray's Test Examples, with Answers. Ray's Higher Arithmetic. Ray's Key to Higher Arithmetic. Ray's Key to New Algebras. PREPARING. Ray's Trigonometry and Mensuration, with Tables. Ray's Analytical Geometry and Conic Sections. Entered, according to Act of Congress, in the year 1866, by SARGENT, WILSON & HINKLE, In the Clerk's Office of the District Court of the United States, for the Southern STEREOTYPED AT THE FRANKLIN TYPE FOUNDRY, CINCINNATI. PREFACE. THIS work has been prepared with a view to meeting the wants of the primary and intermediate departments of large graded schools. The author has also sought to furnish a small, simple, and cheap class-book, adapted to the requirements of pupils commencing the study of Practical Arithmetic in the common schools of the country, as well as in the graded schools of the larger towns and cities. In entering upon the study of Practical Arithmetic, as presented in the more extended works in general use, the mind of the young learner is often confused and embarrassed by a multiplicity of methods, explanations, solutions, rules, exceptions, remarks, notes, etc. To avoid this evil, it has been the constant aim, in the preparation of this work, to present each subject in one form only, and that the most concise and simple consistent with clearness. In treating each subject, a MODEL, designed to be thoroughly studied by the pupil, is given, embracing a full and lucid solution of an example, with accompanying operation, from which a general rule is deduced. The definitions are plain and simple, and as brief as mathematical exactness will admit. Mental exercises precede the practical examples, which, without being unnecessarily multiplied, are sufficiently numerous, especially in the fundamental rules, to give the pupil a thorough drill, rendering him ready, quick, and accurate in the simpler arithmetical calculations. It is not expected that the solutions and explanations given will, in all cases, preclude the necessity of additional illustra tion on the part of the teacher. No book can present a subject so fully as to make it clear to every mind; and it should be the constant endeavor of the teacher to ascertain just what part the pupil fails to understand, and aid him by suggestion, rather than by exhaustive explanation. The late action of Congress, authorizing the use of the Metrical System of Weights and Measures in this country, has rendered it necessary to introduce into American school-books an explanation of this subject. Based on the decimal system, its treatment properly follows decimal fractions. The chapter on the Metrical System has been compiled chiefly from late French works, and has been critically revised by H. A. NEWTON, Professor of Mathematics in Yale College. We take great pleasure in acknowledging our obligations to PROF. NEWTON, whose unwearied exertions in favor of the adoption of the Metric System in this country, entitles him to the cordial thanks of all friends of educational progress. CINCINNATI, Oct. 1866. |