October lo, 1890.] 



SCIENCE. 



209 



derelopment of the theory, whether gfreat or small. For many 

 years the theory seemed to belong especially to German mathe- 

 mali ians ; but the author believes that he has overlooked little of 

 importance, and that he has been impartial in his treatment of 

 the subject. 



An Introduction to the Logic of Algebra. By Ellert W. Davis. 

 New York, Wiley. 8°. $1.50. 



As the author puts it, this book is precisely described by the 

 title, and is mainly the outgrowth of a conviction that the logic of 

 algebra is a very much neglected study. We believe it to be the 

 conviction of many teachers of mathematics that one trouble with 

 students in failing to understand the subject is that they look too 

 far. Each step in mathematical reasoning is simple in itself, and 

 the difficulty comes in in deciding what shall be the next stpp in 

 any process of mathematical reasoning. 



Professor Davis, who is, by the way, the professor of mathe 

 matics in the University of South Carolina, has certainly produced 

 a unique book, and one that will be of great interest to teachers 

 of algebra; but the question naturally occurs to one that possibly 

 he may have niade to appear complicated what heretofore has 

 been more or less readily accepted by students. It is quite true 

 that the processes of algebra are simple and easily taught, and 

 that they are taught mainly for the sake of the processes rather 

 than for the sake of the discipline, — that is, they are taught for 

 the uses to which they ma)' be put, — and it is to be feared that if 

 too much attention is paid to the reasoning which underlies the 

 processes, which has been generally slurred over or even abso- 

 lutely ignored, the student may think there is more in it than 

 there really is, and become correspondingly confused. 



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