HIGHER ARITHMETIC OR THE SCIENCE AND APPLICATION OF NUMBERS COMBINING THE ANALYTIC AND SYNTHETIC MODES OF INSTRUCTION. DESIGNED FOR ADVANCED CLASSES IN SCHOOLS AND ACADEMIES. BY JAMES B. THOMSON, A.M., AUTHOR OF MENTAL ARITHMETIC; EXERCISES IN ARITHMETICAL ANALY! TWENTY FIFTH EDITION. NEW-YORK: PUBLISHED BY NEWMAN AND IVISON, CINCINNATI: MOORE & ANDERSON. AUBURN: J. C. IVISON & 00 1853. FOR SCHOOLS AND ACADEMIES. ners. 1. MENTAL ARITHMETIC; or, First Lessons in Numbers ;—for BeginThis work commences with the simplest combinations of numbers, and gradually advances to more difficult combinations, as the mind of the learner expands and is prepared to comprehend them. II. PRACTICAL ARITHMETIC; - Uniting the Inductive with the Synthetic mode of Instruction; also illustrating the principles of CANCELATION. The design of this work is to make the pupil thoroughly acquainted with the reason of every operation which he is required to perform. abounds in examples, and is eminently practical. It III. KEY TO PRACTICAL ARITHMETIC;-Containing the answers with numerous suggestions, &c. IV. HIGHER ARITHMETIC; or, the Science and Application of Numbers;-For advanced Classes. This work is complete in itself, commencing with the fundamental rules, and extending to the highest department of the science. V. KEY TO HIGHER ARITHMETIC;-Containing all the answers, with many suggestions, and the solution of the more difficult questions. VI. THOMSON'S DAY'S ALGEBRA;-This work is designed to be a lucid and easy transition from the study of Arithmetic to the higher branches of Mathematics. The number of examples is much increased; and the work is every way adapted to the improved methods of instruction in Schools and Academies. VII. KEY TO THOMSON'S DAY'S ALGEBRA;-Containing the answers, the solution of the more difficult problems, &c. VIII. THOMSON'S LEGENDRE'S GEOMETRY;-With practical notes and illustrations. This work has received the approbation of many of the most eminent Teachers and Practical Educators. IX. PLANE TRIGONOMETRY, AND THE MENSURATION OF HEIGHTS AND DISTANCES; with a summary view of the Nature and Use of Logarithms ;-Adapted to the method of instruction in Schools and Academies. X. ELEMENTS OF SURVEYING;-Adapted both to the wants of the learner and the practical Surveyor. (Published soon.) Entered according to Act of Congress, in the year 1847, in the Clerk's Office of the Northern District of New York. PREFACE. THE Higher Arithmetic which is now presentea to the public, is the third and last of a series of Arithmetics adapted to the wants of different classes of pupils in Schools and Academies. The title of each explains the character of the work. The series is constructed upon the principle, that "there is a place for everything, and everything should be in its proper place." Each work forms an entire treatise in itself; the examples in each are all different from those in the others, so that pupils who study the series, will not be obliged to purchase the same matter twice, nor to solve the same problems over again. The Mental Arithmetic, is designed for children from six to eight years of age. It is divided into progressive lessons of convenient length, beginning with the simplest combinations of numbers, and advancing by gradual steps, to more difficult operations, as the mind of the learner expands and is prepared to comprehend them. The Practical Arithmetic embraces all the subjects requisite for a thorough business education. The principles and rules are carefully analyzed and demonstrated; the examples for practice are numerous, and the observations and notes contain much information pertaining to business matters, not found in other works of the kind. This is the FIRST SCHOOL BOOK in which the Standard Units of Weights and Measures adopted by the Government in 1834, were published. The Higher Arithmetic is designed to give a full development of the philosophy of Arithmetic, and its various applications to commercial purposes. Its plan is the following: 1. The work is complete in itself. It commences with notation, and illustrating the different properties of numbers, the principles of Cancelation, and various other methods of contraction, extends to the higher operations in mercantile affairs, and the more abstruse departments of the science. 2. Great pains have been taken to render the definitions and rules clear, concise, exact, comprehensive. 3. It has been a cardinal point never to anticipate a principle; and never to use one principle in the explanation of another, until it has itself been explained or demonstrated. 4. Nothing is taken for granted which requires proof. Every principle therefore has been reinvestigated, and carefully analyzed. 5. The principles are arranged consecutively, and the dependence of each on those that precede it, is pointed out by references. Treated in this manner, the science of Arithmetic presents a series of principles and propositions alike harmonious and logical; and the study of it cannot fail to exert the happiest influence in developing and strengthening the reasoning powers of the learner. 6. The rules are demonstrated with care, and the reasons of every oper ation fully illustrated. 7. The examples are copious and diversified; calling every principle into exercise, and making its application thoroughly understood. 8. In the arrangement of subjects, the natural order of the science has been carefully followed. Common Fractions have therefore been placed immediately after Division, for two reasons. First, they arise from division, and a connexion so intimate should not be severed without cause. Second, in Reduction and the Compound Rules, it is often necessary to multiply and divide by fractions, to add and subtract them, also to carry for them, unless perchance the examples are constructed for the occasion, and with special reference to avoiding these difficulties. For the same reason Federal Money, which is based upon the decimal notation, is placed after Decimal Fractions; Interest, Commission, &c., after Percentage. To require a pupil to understand a rule before he is acquainted with the principles upon which it is based, is compelling him to raise a superstructure, before he is permitted to lay a foundation. 9. In preparing the Tables of Weights and Measures, no effort has been spared to ascertain those in present use in our country; and rejecting such as are obsolete, we have introduced the Standard Units adopted by the Government, together with the methods of determining and applying those standards. 10. Great labor has also been expended in preparing full and accurate Tables of Foreign Weights and Measures, and Moneys of Account, and in comparing them with those of the United States. Such is a brief outline of the present work. In a word, it is designed to be an auxiliary to the teacher, a lucid and comprehensive text-book for the pupil, and an acceptable acquisition to the counting-room. It contains many illustrations and principles not found in other works before the public, and much is believed to be gained in the method of reasoning and analysis. No labor has been spared to render it worthy of the marked favor with which the former productions of the author have been received. J. B. THOMSON. New York, August, 1847. |