ARITHMETICAL ANALYSIS; OR, HIGHER MENTAL ARITHMETIC FOR ADVANCED CLASSES. BY JAMES B. THOMSON, LL.D., AUTHOR OF MENTAL ARITHMETIC; SLATE AND BLACKBOARD EXERCISES; NEW YORK: CLARK & MAYNARD, 5 BARCLAY ST. CHICAGO: S. C. GRIGGS & CO. 1867. Ke 11292 DAY & THOMSON'S MATHEMATICAL SERIES, FOR SCHOOLS AND ACADEMIES. L ARITHMETICAL TABLES. For Primary Schools. Revised and Enlarged. II. MENTAL ARITHMETIC; or, First Lessons in Numbers. For Children. Revised and Enlarged. III. RUDIMENTS OF ARITHMETIC; or, Exercises for the Slate and Black-board. For Beginners. Revised and Enlarged. IV. ARITHMETICAL ANALYSIS; or, Higher Mental Arithmetic. Being a Sequel to Thomson's First Lessons in numbers. For Advanced Classes. V. PRACTICAL ARITHMETIC-Uniting the Inductive with the Synthetic mode of Instruction; also illustrating the Principles of CANCELLATION. Revised and Enlarged. V1. KEY TO PRACTICAL ARITHMETIC. Revised and Fnlarged. For Teachers. VII. HIGHER ARITHMETIC; or, the Science and Application of Numbers. For Advanced Classes in Schools and Acade mies. This work is designed to develop the Philosophy and Applications of Arithmetic. VIII. KEY TO HIGHER ARITHMETIC. For Teachers. IX. THOMSON'S DAY'S ALGEBRA. Being a School Edition of DAY'S LARGE ALGEBRA, with many new Illustrations, and the number of examples much increased. X. KEY TO THOMSON'S DAY'S ALGEBRA. For Teachers. XI. THOMSON'S LEGENDRE'S GEOMETRY: with Practical Notes and Illustrations. XII. ELEMENTS OF TRIGONOMETRY, MENSURATION, AND LOGARITHMS. XIII. ELEMENTS OF SURVEYING. (Published soon.) ENTERED, according to Act of Congress, in the year 1854, In the Clerk's Office of the Southern District of New York. PREFACE. MENTAL ARITHMETIC, as a distinct branch of study, is of recent origin; and we apprehend its value and extent of application are far from being understood, or appreciated. As a means of intellectual discipline, of awakening thought, and strengthening the reasoning powers of the young, it is unsurpassed-perhaps is unequaled by any other branch. A thorough course in mental arithmetic is also the shortest road to a competent knowledge of written arithmetic and the higher branches of mathematics. Nor is its practical influence as a preparation for the common, extemporaneous duties of life, unimportant, or easily measured It gives an independence and self reliance, an accuracy and promptness in business transactions, which can be obtained from no other source. A young man well versed in mental arithmetic, has a 66 computing scale," which the "tricks of the trade" cannot deceive; a scale which is always at hand, and in order, and is worth a thousand-fold more than all the artificial "ready reckoners," which the prolific brain of quackery and avarice ever invented. To secure these important advantages, it is obvious that the study of mental arithmetic must not only be commenced early, but must be continued by the pupil, at least as an occasional exercise, throughout his school-going days. But here we are often met with the objection, that larger and more advanced pupils become disgusted with books which treat of counting their "fingers and thumbs," and adding the "balls upon the Numerical Frame," or stars and other unit marks;" consequently, they cannot be prevailed upon to continue this study. |