THE NATIONAL SERIES OF STANDARD SCHOOL-BOOKS. 



BARNES'S NEW MATHEMATICS. 



In this series JOSEPH FICKLIN, Ph. D., Professor of Mathematics and Astronomy 

 in the University of Missouri, has combined all the best and latest results of practical 

 and experimental teaching of arithmetic with the assistance of many distinguished 

 mathematical authors. 



Barnes's Elementary Arithmetic. 

 Barnes's National Arithmetic. 



These two works constitute a complete arithmetical course in two books. 



They meet the demand for text-books that will help students to acquire the greatest 

 amount of useful and practical knowledge of Arithmetic by the smallest expenditure of 

 time, labor, and money. Nearly every topic in Written Arithmetic is introduced, and its 

 principles illustrated, by exercises in Oral Arithmetic,. The free use of Initiations ; the 

 concise method of combining and treating Properties of Numbers; tin- treatment of 

 Multiplication and Division of Fractions in two cases, and then reduced to une; Can- 

 cellation by the use of the vertical line, especially in Fractions, Interest, and Proportion; 

 the brief, simple, and greatly superior method of working Partial Payim-nts l>y the 

 "Time Table "and Cancellation ; the substitution of formulas to a great extent lor 

 rules; the full and practical treatment of the Metric System, &c., indicate their com- 

 pleteness. A variety of methods and processes for the same topic, which deprive the 

 pupil of the great benefit of doing a part of the thinking and labor for himself, have 

 been discarded. The statement of principles, definitions, rules, &c., is brief and simple. 

 The illustrations and methods are explicit, direct, and practical. The ureat number 

 and variety of Examples embody the actual business of the day. The very large 

 amount of matter condensed in so small a compass has been accomplished \<\ econo- 

 mizing every line of space, by rejecting superfluous matter and obsolete terms, and by 

 avoiding the repetition of analyses, explanations, and operations in the advanced topics 

 which have been used in the more elementary parts of these books. 



AUXILIARIES. 



For use in district schools, and for supplying a text-book in advanced work for 

 classes having finished the course as given in the ordinary Practical Arithmetics, the 

 National Arithmetic has been divided and bound separately, as follows : 



Barnes's Practical Arithmetic. 



Barnes's Advanced Arithmetic. 



In many schools there are classes that for various reasons never reach beyond 

 Percentage. It is just such cases where Barnes's Practical Arithmetic will answer a 

 good purpose, at a price to the pupil much less than to buy the complete book. On the 

 other hand, classes having finished the ordinary Practical Arithmetic can proceed 

 with the higher course by using Barnes's Advanced Arithmetic. 



For primary schools requiring simply a table book, and the earliest rudiments 

 forcibly presented through object-teaching and copious illustrations, we have 

 prepared 



Barnes's First Lessons in Arithmetic, 



which begins with the most elementary notions of numbers, and proceeds, by simple 

 steps, to develop all the fundamental principles of Arithmetic. 



Barnes's Elements of Algebra. 



This work, as its title indicates, is elementary in its character and suitable for use, 

 (1) in such public schools as give instruction in the Elements of Algebra : (2) in institu- 

 tions of learning whose courses of study do not include Higher Algebra ; (3) in schools 

 whose object is to prepare students for entrance into our colleges and universities. 

 Ihis book will also meet the wants of students of Physics who require some knowledge of 



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