THE PROGRESSIVE HIGHER ARITHMETIC, FOR SCHOOLS, ACADEMIES, AND MERCANTILE COLLEGES. COMBINING THE ANALYTIC AND SYNTHETIC METHODS; AND FORMING A COMPLETE TREATISE ON ARITHMETICAL BUSINESS APPLICATIONS. BY HORATIO N. ROBINSON, LL. D., AUTHOR OF WORKS ON ALGEBRA, GEOMETRY AND TRIGONOMETRY, SURVEYING AND NEW YORK: IVISON, PHINNEY, BLAKEMAN & CO. CHICAGO: S. C. GRIGGS & CO. 1868. Series of Mathematics, The most COMPLETE, most PRACTICAL, and most SCIENTIFIC SERIES of MATHEMATICAL TEXT-BOOKS ever issued in this country. (IN TWENTY-TWO VOLUMES.) Robinson's Progressive Table Book, Robinson's Progressive Primary Arithmetic, - Robinson's Arithmetical Examples, Robinson's Key to Elementary Algebra, - Robinson's Key to University Algebra, Robinson's New University Algebra, Robinson's Key to New University Algebra, Robinson's New Geometry and Trigonometry, Robinson's Surveying and Navigation, Robinson's Analyt. Geometry and Conic Sections, Robinson's Differen. and Int. Calculus, Kiddle's New Elementary Astronomy, Robinson's University Astronomy, Robinson's Mathematical Operations, Robinson's Key to Geometry and Trigonometry, Conic Entered, according to Act of Congress, in the year 1860, by DANIEL W. FISH & J. H. FRENCH, 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 Northern District of the New York. Education [per croft Library PREFACE. R559 Educ. Lib THIS work is intended to complete a well graded and progressive series of Arithmetics, and to furnish to advanced students a more full and comprehensive text-book on the Science of Numbers than has before been published; a work that shall embrace those subjects necessary to give the pupil a thoroughly practical and scientific arithmetical education, either for the farm, the workshop, or a profession, or for the more difficult operations of the countingroom and of mercantile and commercial life. There are two general methods of presenting the elements of arithmetical science, the Synthetic and the Analytic. Comparison enters into every operation, from the simplest combination of numbers to the most complicated problems in the Higher Mathematics. Analysis first generalizes a subject and then develops the particulars of which it consists; Synthesis first presents particulars, from which, by easy and progressive steps, the pupil is led to a general and comprehensive view of the subject. Analysis separates truths and properties into their elements or first principles; Synthesis constructs general principles from particular cases. Analysis appeals more to the reason, and cultivates the desire to search for first principles, and to understand the reason for every process rather than to know the rule. Hence, the leading method in an elementary course of instruction should be the Synthetic, while in an advanced course it should be the Analytic. The following characteristics of a first class text-book will be obvious to all who examine this work: the typogra(ii) M645483 |