July 22, 1910] 



SCIENCE 



115 



As a rule, bibliographical works, tbougb 

 valuable, are uninteresting. The publication 

 which we are reviewing is an exception to the 

 general rule; it is interesting as well as val- 

 uable. Every college and school library ought 

 to possess a copy of it. The author aims not 

 only to catalogue the arithmetics in Mr. 

 Plimpton's library that were published before 

 ' 1601 and give a brief statement of their con- 

 tents, but to supplement this by the titles of 

 other arithmetics known to have been printed 

 during that period. Altogether not less than 

 500 publications are given, a number which 

 swells to 1,200, if the various editions of each 

 publication are counted. In addition to this 

 a large number of manuscripts, some belong- 

 ing to the thirteenth century, are catalogued 

 and described. Perhaps no period in the his- 

 tory of aritlimetic is more important than the 

 fifteenth and sixteenth centuries, when printed 

 works came to be widely used and when dif- 

 ferent methods of reckoning were struggling 

 for supremacy. 



What makes this book specially interesting 

 are the numerous protographs of the title- 

 pages, and of other pages exhibiting the nota- 

 tion and methods of computation in arith- 

 metic, in vogue four or five centuries ago. 

 The reader has before him in photographic 

 reproduction the old scratch methods of mul- 

 tiplication and division, the beginnings of 

 decimal fractions, documents showing the 

 probable origin of the -|- and — signs, draw- 

 ings explaining various kinds of finger sym- 

 bolism and many other points of interest to 

 teachers and students of arithmetic. 



In America few researches have been carried 

 on in the history of mathematics. One needs 

 only examine the volumes of the Bibliotheca 

 Mathematica, a journal devoted to the history 

 of mathematics, to realize the dearth of Amer- 

 ican productive scholarship in this field. With 

 this fact in view it is a pleasure to note that 

 the above publication is one of value and im- 

 portance, when measured by European stand- 

 ards. Sixty years ago De Morgan's "Arith- 

 metical Books " was the best authority on 

 arithmetical bibliography. Later much work 

 in this line was done on the European conti- 

 nent. Now Professor Smith's " Eara Arith- 



metica " takes first rank. Professor Smith 

 has enjoyed unusual facilities for the prepara- 

 tion of this work. The Plimpton collection of 

 fifteenth and sixteenth century aritlmietics, in 

 New York City, the largest collection of this 

 kind that has ever been made, lay at his dis- 

 posal. He has labored assiduously and with 

 care. Here and there we might have wished 

 to have seen a still wider range of topics 

 selected for photographic exhibition; in one 

 or two instances a greater watchfulness for the 

 historically vital points in books might have 

 been desired. But these are minor blemishes. 

 The work as a whole takes first place as a 

 bibliography of early printed arithmetics. 



Florian Cajori 



Thought and Things or Genetic Logic} Vol. 

 II., Experimental Logic. James Mark 

 Baldwin. London, Swan Sonnenschien & 

 Co.; New York, The Macmillan Company. 

 1908. Pp. XV + 436. 



This is the second of three volumes on a 

 subject never before so comprehensively 

 treated by an American author. The title of 

 the present volume has been in use for some 

 time, but the treatment is peculiar. The 

 genetic method of tracing out the various steps 

 and stages in the embodiment of belief is 

 more consistently followed here than, I think, 

 in any well-known treatise on logic. Great 

 praise is due the work for this and for many 

 interesting and illuminating points in the dis- 

 cussion. The general problem of the work is 

 logic from the knower's point of view, not 

 logic from the point of view of . the outside 

 psychologist or logician who looks on and 

 analyzes. The theme itself as conceived by 

 Baldwin presupposes a difference between 

 these two types of logic: it presupposes that 

 knowledge and the knowing process have for 

 the knower characters which they do not have 

 for the " outsider." Knowing, for the knower, 

 involves continual reference, according to 

 Baldwin, to similar knowing processes dealing 

 with the same material and going on actually 

 or possibly in other minds; it involves, in 

 ^ The entire work is appearing simultaneously 

 in French, German and English. It includes a 

 fair index to volumes one and two, and three 

 appendices. 



