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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 resembled 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 remembered 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 investigator. 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 Jahrbuch ├╝ber 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 astronomy; and it is an interesting coincidence that the International Catalogue should have established a quadrivium of pure mathematics, as was observed above.

Among the general terms of classification, that of analysis is probably 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