324 POPULAR SCIENCE MONTHLY 



fication yet the number of such terms may become so large as to justify 

 the criticism of Hankel that the stately mathematical structure re- 

 sembled the tower of Babel. The proper time for the introduction 

 of new technical terms and new heads of classification must depend 

 upon the good judgment of the workers in this field, it being remem- 

 bered that terms and classifications are secondary matters, although by 

 no means useless, and that the main thing is to extend the domain of 

 knowledge, especially where the beauty or usefulness of the results 

 assure them a permanent place in the intellectual wealth of the world. 



A large variety of classifications may prove serviceable to the in- 

 vestigator. Sometimes an author's catalogue may render the best 

 service, while at another the grouping together of a large number 

 of related things as is done in the Jalirbuch uber die Fortschritte der 

 Mathematik, where pure mathematics is divided into only fifty parts, 

 renders the most valuable service. At still another time, the dictionary 

 arrangement under thousands of terms, as it appears in the indexes of 

 large works, especially in the incomplete encyclopedia to which we 

 referred above, offers the most convenient method of arriving at the 

 desired information. Fortunately the current mathematical literature 

 is now being classified according to several different methods, each 

 possessing peculiar advantages for the different needs of the scholar. 



The history of classification in mathematics is very old as may be 

 seen from the fact that the mathematical handbook of Ahmes, which 

 was written about 1700 B. C, already contains the divisions into 

 arithmetic, and plane and solid geometry. As this work bears the title 

 " Directions for obtaining a knowledge of all dark things," it would 

 appear that the observance of the distinction between arithmetic and 

 geometry may have been older than of that which separates mathematics 

 from the other sciences. In fact, even at the time of Plato, the term 

 mathematics included all scientific instruction and its more restrictive 

 meaning seems to have had its origin in the Peripatetic School. The 

 main divisions of the mathematical sciences during the Greek period 

 were: logistica, arithmetic, plane and solid geometry, music and 

 astronomy. One of the best known classifications of mathematics is the 

 Quadrivium of Boethins, viz., arithmetic, music, geometry and astron- 

 omy; and it is an interesting coincidence that the International Cata- 

 logue should have established a quadrivium of pure mathematics, as was 

 observed above. 



Among the general terms of classification, that of analysis is prob- 

 ably the least familiar to the non-mathematician. All have some idea 

 of arithmetic, algebra and geometry from the context of elementary 

 text-books bearing these names, but it is not customary to place the 

 term analysis on the cover of an elementary text-book in the English 

 language. Perhaps this is due, in part, to the fact that our secondary 



