PROGRESSIVE INTELLECTUAL ARITHMETIC; ON THE INDUCTIVE PLAN. BEING A SEQUEL TO THE PROGRESSIVE PRIMARY ARITHMETIC, CONTAINING AND DESIGNED FOR THE MORE ADVANCED CLASSES IN COMMON SCHOOLS AND ACADEMIES. EDITED BY DANIEL W. FISH, A.M. IVISON, BLAKEMAN, TAYLOR & CO., PUBLISHERS, NEW YORK AND CHICAGO. 1877. ROBINSON'S Mathematical Series. Graded to the wants of Primary, Intermediate, Grammar, 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. New Surveying and Navigation. New Differential and Integral Calculus. University Astronomy--Descriptive and Physical. Key to Geometry and Trigonometry, Analytical Geometry and Conic Sections, 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 Northern District of New York. NARYAND COLLEGE LIPSARY BY EXCHANGE FROM FEE 27 1932 PREFACE. THE importance, and the practical benefit to be derived from the study of Intellectual Arithmetic, not only as a preparation for business life, but as a means of developing and strengthening the thinking and reasoning powers, and of thorough mental culture, can not be over-estimated. Not only is it a necessary study for young pupils, but indispensable to the more advanced student, as a preparation for the prompt and accurate business man. is believed that, as a general rule, the most critical, correct, and And it ready students of mathematics are those who have been most thoroughly drilled in intellectual arithmetic. This work has been prepared more especially for advanced classes, and is designed for those who have first been well taught in the primary book, and for such as are pursuing the study of written arithmetic, or algebra, and who have never been thoroughly exercised in this branch of study. Only a few of the many points of difference between this and other similar works, and which, it is believed, renders this superior to them, will be referred to. It is more complete, comprehensive, and progressive in its character. The arrangement and classification are more strictly sys tematic, and in accordance with the natural order of mathematical science. The development of principles, and their applications, are shown by a more numerous selection, and greater variety of appropriate examples, progressively arranged, commencing with those that are simple and easy, and advancing to those more complex and difficult. At intervals, and especially in the closing sections of each chapter, examples are given containing such a combination of principles, and forms of analysis, as to require a knowledge of almost every principle previously taught, thus affording the pupil a thorough review, as well as requiring him to classify his knowledge of what he has been over. One of the most important, and, it is thought, one of the most original and useful features of this work, is the full, concise, and uniform system of ANALYSIS it contains, rience in the school-room. the result of long expe Particular attention is invited to the subjects of Fractions, Per centage, and Interest; their treatment is peculiar, and adapted to obviate many of the difficulties, and greatly abbreviate most of the operations in them. (8) The chapter of Miscellaneous Examples will afford a valuable and thorough drill to the advanced student of arithmetic or algebra. They contain a great variety of principles, and while they may be considered difficult, yet the full analysis given of every principle, and the selection of numbers so adapted to the conditions of the question as to produce results free from large and difficult fractions, will render a mental solution of them comparatively easy. In conclusion, we may be allowed to express the belief, that in this work the thorough teacher will find a desideratum long sought in this department of science,-the means of mental discipline and development such as has been furnished by no similar treatise. THE AUTHOR. SUGGESTIONS TO TEACHERS. Pupils of nearly the same degree of advancement should be classed together. Regular exercises should be assigned to the class, and sufficient time allowed them to thoroughly examine their lesson before being called upon to recite. The use of the book at the time of recitation should be strictly prohibited, except, perhaps, in some of the more difficult lessons in the latter part of the work. Each example should be read but once, slowly and distinctly, the pupils called upon promiscuously, who should arise, stand erect, repeat the example, and then give the analysis. This will secure close attention. Every question should be clearly and thoroughly analyzed, and the pupil required to adhere strictly to the forms of solution given, unless better ones can be substituted; and in no case should he be allowed to omit the conclusion, commencing with "Therefore." The class should be encouraged to detect and correct errors in statement or analysis, to criticise and make proper inquiries, all of which should be signaled by the uplifted hand. It is suggested that the class be occasionally exercised upon "Ringing the Changes," as explained in the Appendix, and which may be applied to a great number and variety of examples. It will not only afford a valuable drill, but a pleasant and enlivening exercise. INTELLECTUAL ARITHMETIC. CHAPTER I. ADDITION. 1. 1. JAMES had 1 cent, and his father gave him 1 more; how many had he then? 2. If a slate pencil cost 2 cents, and a steel pen 1 cent, how many cents will both cost? 3. George spent 2 cents for candy, and had 2 cents left; how many cents had he at first? 4. A farmer sold a calf for 3 dollars, and a pig for 2 dollars; how many dollars did he receive for both? 5. Mary gave 2 cents for some tape, and 5 cents for a thimble; how many cents did she give for both? 6. Martin gave John 3 apples, and kept 4 for himself; how many apples had he at first? 7. There are 4 books on one desk, and 2 books on another; how many books on both desks? 8. If a lemon cost 3 cents, and an orange 5 cents, how many cents do both cost? 9. In a certain class there are 5 girls and 4 boys; how many pupils in the class? 10. Samuel had 3 marbles, and his brother gave him 3 more; how many did he then have ? 11. Bought a barrel of apples for 2 dollars, and a cord of wood for 4 dollars; how many dollars did both cost? |