406 Notices respecting New Books. 



character of the several methods is examined, in connexion with 

 the phenomena of the human mind. The character of our first prin- 

 ciples, and the logic of the early theorems of each branch of pure 

 mathematics, are proposed by this class of philosophers as the im- 

 mediate subjects of their investigation. The other class, and that the 

 more influential and learned one, proposes to discover the influence 

 of methods of research upon the progress of discovery, to classify 

 our knowledge according to its bearing upon this one point, and to 

 generalize, as far as possible, the isolated and incompletely connected 

 propositions which are already known. 



Of this latter class M. Chasles is a splendid example ; and of the 

 former, Mr. Newman is a very respectable and (which renders it of 

 more value) a very useful one. 



The " off-handed " manner in which the fundamental principles 

 of geometry are generally dismissed by systematic writers on the 

 subject, is essential to the general style and objects with which such 

 works are composed, namely, the most brief development of the 

 greatest possible number of geometrical truths in a given space. 

 Still, we think that the general purposes of mental culture would 

 be better studied in making geometry merely one of the illustrations 

 of the phenomena of mind : and in this Mr. Newman has evidently 

 entertained the same views that we do, and as was so forcibly urgecj 

 by that distinguished master of the philosophy of the human mind, 

 Dugald Stewart ; though perhaps we differ from each of them, as they 

 do from each other, on certain points brought under discussion. 



In a notice like the present, it would be impossible to give any 

 idea of the details of the work. We would moreover remark, that to 

 the discussion of the fundamental principles of the geometry of the 

 school of Euclid our approbation and recommendation is mainly con- 

 fined. When the author travels beyond these boundaries he is evi- 

 dently " not at home," as his acquaintance with the higher branches 

 of modern geometry is evidently very limited, and his criticisms, 

 therefore, of little value. We can, however, with this reservation, 

 and without pledging ourselves to the entire adoption of the author's 

 views and reasonings, most cordially recommend the perusal of the 

 book to the speculative geometer, and urge its careful study upon 

 those who are engaged in teaching the elements of the science for 

 the purpose of cultivating the faculties, rather than of " creating 

 mathematicians by profession." 



Logarithmic and Trigonometric Tables, %c. London : Simpkin and 

 Marshall, 1836. 

 Six years ago a private gentleman residing in the country caused 

 to be printed an edition of Hassler's Logarithmic Tables. By 

 various causes the advertisement of this book was delayed, so that 

 up to the present time it has remained altogether unknown, even to 

 those who take pleasure in collecting and comparing tables. On 

 these facts coming to the knowledge of the writer of this paragraph, 

 he recommended that, considering the length of time which had 

 elapsed, the work should not be brought into notice without some 



