HIG H E R A RITHMETIC; 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 ANALYSIS, LEGENDRE'S GEOMETRY, ETC. NEW YORK: No. 199 BROADWAY. DAY AND THOMSON'S MATHEMATICAL SERIES. FOR SCHOOLS AND ACADEMIES, ners. TION. I. MENTAL ARITHMETIC; or, First Lessons in Numbers ;—for Begin This 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 CANCELA The design of this work is to make the pupil thoroughly acquainted with the reason of every operation which he is required to perform. It abounds in examples, and is eminently practical. 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. Th 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, BY JAMES B. THOMSON, Stereotyped by Thomas B. Smith, 216 William St. N Y. PREFACE. The Higher Arithmetic which is now presented 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 tille 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, ånd carefully analyzed. |