240 Notices respecting New Books. 



no English mathematical master has as jet ventured to teach to 

 any class of school-boys, but we would not on that account brand 

 the little work referred to as a failure; on the contrary, we pro- 

 nounce it to be a most suggestive book for teachers, and possibly 

 for students who have left school-days far behind. The book under 

 notice was brought into existence as a Syllabus by an Association of 

 Mathematical teachers, and has been nurtured by them until its suc- 

 cess in its original form as a means of getting geometrical ideas into 

 the heads of junior pupils has been such as to lead to the demand for 

 the clothing of the bare bones of a Syllabus in the present decent 

 garb in which these ' Elements ' now appear. 



We fear that this latest form, however, will be no more accept- 

 able to our critic than the antecedent forms, and that he will still 

 pronounce upon the Association's work the dictum, " the result is 

 not as satisfactory as might have been wished." Certainly " there 

 is very little of the influence of modern ideas to be found " here, 

 and " for modern methods one looks in vain." Deluded mathe- 

 matical teachers ! who still prefer " stare super antiquas vias," why 

 do you not burst the Cantabrigian bonds and be willing " jurare in 

 verba magistri," — that master, of course, being Steiner? The 

 age is not ripe, we fear, for such teaching. Our own experience, 

 which dates from the consulship of Plancus, is that one or two in 

 a hundred pupils might appreciate the high Alps of the modern 

 methods, but the rest must be kept down to the lower pastures. 

 " Faithful are the wounds of a friend ! " and that our Critic is a 

 friend is clear from his parting words. " Nevertheless, it is satis- 

 factory to see that the use of the Syllabus on Plane Geometry has 

 spread pretty widely, and it is to be hoped that it will continue to 

 do so. A thorough reform, in the direction indicated, will be a 

 difficult task, and it will perhaps be a long time before it is pos- 

 sible." Much will be done by the work he himself is doing in our 

 midst. Now a word or two on the book itself. We have read 

 from Theorem ii. to the end with much interest. Into a well-worn 

 subject the Committee have infused much freshness of treatment ; 

 the arrangement appears to us excellent ; and the collection of 

 Exercises admirably chosen. All these opinions are formed with 

 reference to the purpose for which the work has been drawn up. 

 For advanced pupils the exercises would in many cases be too ele- 

 mentary ; but for the ordinary members of our classes they are 

 capitally graduated, and many a boy ought to be lured on by the 

 ability of getting out " riders " for himself. We have always hesi- 

 tated over Theorem i., which is, " All right angles are equal to one 

 another." The compilers, doubtless after some considerable debate, 

 have gone in for a long proof of this, instead of getting it from the 

 Obs. to def. 10, " A straight angle is equal to two right angles." 

 But this is a point of no great importance, as any teacher is free to 

 substitute a proof founded on the " Obs.," or any other proof, for 

 the one in the text. The rest, as we have implied, goes off most 

 trippingly. We venture upon a few remarks upon the definitions. 



