PROGRESSIVE PRACTICAL ARITHMETIC; CONTAINING THE THEORY OF NUMBERS, IN CONNECTION WITH CONCISE ANALYTIC AND SYNTHETIC METHODS OF SOLUTION, AND FOR COMMON SCHOOLS AND ACADEMIES. BY DANIEL W. FISH, A.M., AUTHOR OF THE TABLE-BOOK, PRIMARY AND INTELLECTUAL ARITHMETICS, IVISON, BLAKEMAN & COMPANY, PUBLISHERS, NEW YORK AND CHICAGO. PUBLIC LIBRARY 917639 ASTOR, LENOX AND ROBINSON'S Mathematical Series. Graded to the wants of Primary, Intermediate, Gramm-z Normal, and High Schools, Academies, and Colleges Progressive Table Book. Progressive Primary Arithmetic. Progressive Intellectual Arithmetic. Rudiments of Written Arithmetic. JUNIOR-CLASS ARITHMETIC, Oral and Written. NEW.. Progressive Practical Arithmetic. Key to Practical Arithmetic. Progressive Higher Arithmetic. Key to Higher Arithmetic. Key to New Elementary Algebra. New University Algebra. Key to New University Algebra. New Geometry and Trigonometry. In one vol. Geometry, Plane and Solid. In separate vol. Trigonometry, Plane and Spherical. In separate vol. New Analytical Geometry and Conic Sections. New Surveying and Navigation. New Differential and Integral Calculus. University Astronomy-Descriptive and Physical. Key to Geometry and Trigonometry, Analytical Geometry and Conic Sec tions, Surveying and Navigation. Entered, according to Act of Congress, in the year 1858, and again in the year 1863, by DANIEL W. FISH, A.M., In the Clerk's Office of the District Court of the United States, for the Northeu District of New York. Copyright, 1877, by Daniel W. Fish. PREFACE. PROGRESS and improvement characterize almost every art and science; and within the last few years the science of Arithmetic has received many important additions and improvements, which have appeared from time to time successively in the different treatises published upon this subject. In the preparation of this work it has been the author's aim to combine, and to present in one harmonious whole, all these modern improvements, as well as to introduce some new methods and practical operations not found in other works of the same grade; in short, to present the subject of Arithmetic to the pupil more as a science than an art; to teach him methods of thought, and how to reason, rather than what to do; to give unity, system, and practical utility to the science and art of computation. 66 The author believes that both teacher and pupil should have the privilege, as well as the benefit, of performing at least a part of the thinking and the labor necessary to the study of Arithmetic; hence the present work has not been encumbered with the multiplicity of "notes," 'suggestions," and superfluous operations so common to most Practical Arithmetics of the present day, and which prevent the cultivation of that self-reliance, that clearness of thought, and that vigor of intellect, which always characterize the truly educated mind. The author claims for this treatise improvement upon, if not supe1iority over, others of the kind in the following particulars, viz.: In the mechanical and typographical style of the work; the open and attractive page; the progressive and scientific arrangement of the subjects; clearness and conciseness of definitions; fullness and accuracy in the new and improved methods of operations and analyses; brevity and perspicuity of rules; and in the very large number of examples prepared and arranged with special reference to their practical utility, and their adaptation to the real business of active life. Th answers to a part of the examples have been omitted, that the learner may acquire the discipline resulting from verifying the operations. Particular attention is invited to improvements in the subjects of Common Divisors, Multiples, Fractions, Percentage, Interest, Proportion, Analysis, Alligation, and the Roots, as it is believed these articles contain some practical features not common to other authors upon these subjects. The improvements in Percentage made necessary by the financial changes of the last few years are especially noticeable. The different kinds of United States Securities, Bonds, and Treasury Notes are described, and their comparative value in commercial transactions illustrated by practical examples. The difference between Gold and Currency, and the corresponding difference in prices, exhibited in trade, are taught and illustrated, and many other things that every commercial student and business man ought to know and understand. It is not claimed that this is a perfect work, for perfection is impossible; but no effort has been spared to present a clear, scientific, comprehensive, and complete system, sufficiently full for the business man and the scholar; not encumbered with unnecessary theories, and yet combining and systematizing real improvements of a practical and useful nature. How nearly this end has been attained the intelligent and experienced teacher and educator must determine. THE AUTHOR. NOTICE. This book has been newly electrotyped in the latest and best style of typography. No change has been made in the text, except to correct positive errors, drop a few obsolete terms from the tables, and in place of " Gold Investments" and the Colonial Currency of shillings and pence, some practical matter has been substituted. These improvements are designed to give new life to a book that has proved its real merits by the very large circulation it has obtained. BROOKLYN, Jan., 1888. |