458 



SCIENCE 



[N. S. Vol. LIII. No. 1376 



SCIENTIFIC BOOKS 



The Sumario Compendioso of Brother Juan 

 Biez. The earliest mathematical work of 

 the ISTew World. By David Eugene Smith. 

 1921. Boston and London: Ginn and Com- 

 pany. 65 pages. Price $4.00. 



Those who are interested ia the earlier 

 mathematical developments only in so far as 

 it can be shown that these developments have 

 contributed directly to the present extent of 

 our mathematical knowledge will find little 

 to interest them in the present small volume. 

 It is not claimed that this volume exhibits 

 any decided step forward in mathematics or 

 that it exerted a great influence on later works 

 devoted, to the same subject. There are, how- 

 ever, many mathematicians and historians who 

 will doubtless be very glad to have an oppor- 

 tunity to read in their own language the ex- 

 cellent translation which Professor Smith has 

 here provided of what seems to be " the earl- 

 iest mathematical work of the New World." 



It is desirable that the student of the his- 

 tory of arithmetic should be able to consult 

 original sources. By the publication of the 

 " Para Arithmetiea " about a dozen years ago 

 and by the publication of the present volume 

 Professor Smith has rendered very valuable 

 service to those who desire to consult such 

 sources. The historical notes which appear 

 in these works are exceedingly valuable even 

 if they are often less extended than might 

 appear desirable. In the present volume two 

 pages or less of such notes relate to each of 

 the following four subjects: The Mexico of 

 the period, printing established in Mexico, 

 general description of the book, and nature 

 of the tables. 



An important oversight should be noted 

 here in order that the reader may not be mis- 

 led in regard to the time when the book under 

 review, which was first published in 1556, 

 became known to American educators. To 

 establish the fact that the reader is seriously 

 exposed to misconception as regards the point 

 in question and also on account of the interest 

 which these statements may command, we 

 quote the first three sentences of the preface. 



If the student of the history of education were 



asked to name the earliest work on mathematics 

 published hj an American press, he might, after a 

 little investigation, mention the anonymous arith- 

 metic that was printed in Boston in the year 1729. 

 It is now known that this was the work of that 

 Isaac Greenwood who held for some years the chair 

 of mathematics in what was then Harvard College. 

 If he should search the records still farther back, 

 he might come upon the American reprint of 

 Hodder's well-known English arithmetic, the first 

 text-book on the subject, so far as known, to appear 

 in our language on this side the Atlantic. 



As some " student of the history of educa- 

 tion " may be assumed to have read the " Eara 

 Arithmetiea " and noted that on page 286 

 thei'eof the work under review was called " the 

 first arithmetic printed in America " it seems 

 strange that such a student should have been 

 overlooked while the said preface was vraitten. 

 One is perhaps still more surprised to find 

 that such an intelligent student was also over- 

 looked when Professor Smith prepared the ar- 

 ticle relating to the book under review for the 

 last January number of the American Mathe- 

 matical Monthly as well as when he read a 

 pai)er before an intelligent audience during 

 tlae recent meeting of the American Associa- 

 tion for the Advancement of Science at 

 Chicago. On both of these occasions the sub- 

 stance of the part of the preface quoted above 

 was given without any reference to the fact 

 that one of the most interesting elements 

 relating to tlie subject under consideration had 

 been noted a dozen years earlier in the " Eara 

 Arithmetiea." 



The emphasis on this oversight in such a 

 public place seems to be justified by the facts 

 that tliis emphasis may tend to lessen the 

 danger that readers of the book under review 

 will be misled as regards an interesting his- 

 torical fact, and that one could not condemn 

 in too strong terms one of the motives which 

 might possibly be ascribed to the translator 

 and editor by the reader after discovering that 

 he had been misled by the statements quoted 

 above. Being forewarned such a reader is 

 more likely to attribute these statements to 

 an astounding oversight by an unusually 

 painstaking and careful writer. 



Tables make up the greater part of the 

 original work but as they are no longer of 



