72 Notices respecting Nexv Books. 



this country at the present day. It is used, we understand, in all 

 our great Grammar Schools, in the Royal Military Academy, and 

 many other public institutions, as well as in a large number of pri- 

 vate schools. 



The works of Mr. Gaskin all tend to show the power of what is 

 vulgarly in modern times called " analysis " to deal with geometrical 

 propositions. As far as his books can give any insight into his 

 thoughts, it would ap])ear to be his aim to supersede the Greek geo- 

 metry. This may arise however from the circumstance of the other 

 ground being already occupied by Mr. Potts, and his honourable un- 

 willingness to interfere with the objects of his collahorateur ; and we 

 are the more disposed to think so from some speculations in his 

 " Third Appendix to the Solutions of Geometrical Problems," which 

 prove him to possess a considerable share of geometrical j)ower as 

 well as a more than usual share of algebraical. Whatever view be 

 taken of this, we can most cordially award him our praise for the 

 masterly manner in which he has applied algebra to many of the 

 problems in both his volumes ; and in cases too where he had great 

 difficulties to contend against from the unsuitabillty of his instrument 

 for its intended operation. It is a remarkable circumstance that 

 those problems which are most easily resolved by pure geometry give 

 rise to the greatest difficulty and complexity by every method of al- 

 gebraical treatment ; and vice versa. An authority of no mean weight 

 has indeed asserted that in such cases " the fault is not in the analysis, 

 hut in the analyst :" but we may say with the same propriety on the 

 other side, that " the fault is not in the geometry, but the geometer." 

 Be this as it may, in the present state of geometry and algebra, we 

 believe our position will not be generally disputed. Mr. Gaskin, 

 then, has imposed upon himself many artificial difficulties ; whilst on 

 the other hand he has mastered them more completely than we be- 

 lieve any one of his University cotemporaries could have done — more 

 completely, it is certain, than they had ever before been mastered. 

 There are, indeed, isolated exceptions, but these are few ; whilst the 

 great address and ability displayed in the majority of the solutions 

 place Mr. Gaskin amongst the most successful and effective writers 

 on the application of Algebra to Geometry of our age and country. 



Mr. Gaskin's selection of the "problems" given in the " College 

 Papers of St. John's " (containing the " Trigonometrical Problems 

 from 1829 to 1846," and the " Geometrical Problems from 1S30 to 

 1846") is apparently founded on an assumed superiority of the papers 

 given in that College over those given in any other. Upon this point 

 we have no means of judging : but we know that the papers of St. 

 John's are much sought after by the undergraduates (especially on the 

 more elementary subjects), upon which to exercise themselves. Mr. 

 Gaskin's choice is, therefore, in all probability a judicious one ; and 

 as it is a University question rather than a public one, Mr. Gaskin 

 is himself the better judge in such a case. The idea under which 

 the solutions are constructed is well expressed in the preface to the 

 Trigonometrical papers : — " The time allowed for the solution of each 

 paper being limited to about three hours, the author has adopted the 

 method which each example most naturally suggested, in preference to 



