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XL Notices respecting New Books. 



Bistoire des Mathematiques. Par Jacques Boyek. Illustre'e de fac- 

 similes de mauuscrits et de portraits. Paris : Georges Carre et 

 C. Naud, 1900 : pp. xi-f 256. 



npHERE are two ways of writing a history of mathematics. One, 

 -*- which appeals to the general reader, consists in giving copious 

 biographical details of the men to whose genius the science owes 

 its existence, and in referring to their actual contributions to the 

 science in as brief and concise a manner as possible. The other 

 is to assign the chief place to their scientific contributions, and 

 treat their biographies as of secondary importance. Of course, 

 the two methods may be combined, but it seems to us that, if the 

 book is to be kept within moderate limits, the writer will prefer to 

 adopt one or other of the two plans indicated. M. Boyer appears 

 to have chosen the second ; his book is one primarily addressed 

 to the student, and not to the general reader. The treatment is 

 highly compressed, and it is very seldom that the author gives us 

 anything beyond the dates of birth and death and the merest 

 skeleton outline of the careers of the men who have moulded the 

 science : he prefers to reserve his space for an account of their 

 scientific work, and to present that account in as elementary a 

 manner as the nature of the subject will allow. An interesting 

 and puzzling piece of information is contained in the first chapter 

 of the book, where, in giving an account of the recently discovered 

 Babylonian tablets (dating back to 2000 B.C.) containing tables of 

 the squares of the natural numbers, the author points out that the 

 method of notation employed undoubtedly suggests the use of a 

 sexagesimal system ! The illustrations — of which there are 26 — 

 add greatly to the interest of the book ; they are all reproductions 

 of old engravings. The book is beautifully printed, and we have 

 not noticed any typographical errors, with the single exception of 

 p. 1 08, where 4 [2] + 3 [1] should read 3 [2] + 4 [1 J. The book is 

 thoroughly up to date, the last chapter containing a brief sketch 

 of the most recent developments of the science. To anybody 

 wishing to acquire some knowledge of the history of mathematics, 

 the book may be safely recommended as containing the desired 

 information in a very concise form. But we cannot help thinking 

 that the book might have been rendered much more interesting 

 by the introduction of some of those human touches which render 

 Mr. W. W. B. Ball's ' Short History of Mathematics' such delight- 

 ful reading. 



