468 Notices respecting New Books. 



And in consequence the chapter, whatever its merits in other respects, 

 is exceedingly abstruse. It might also be inferred from the defini- 

 tion that it was intended to treat questions of proportionality through 

 the medium of numerical measures ; and, in fact, throughout the third 

 and fourth books pure geometry is as much as possible dispensed with, 

 and a good deal of them consists of what is more commonly termed 

 mensuration, or the application of algebra to geometry. In short, 

 the contents of the third and fourth books are, though very differ- 

 ently treated, in substance nearly the same as a few of the proposi- 

 tions in the second book of Euclid, the sixth book, and the proposi- 

 tions in mensuration deducible from them, together with the mensu- 

 ration of the circle. 



Of the parts of the book particularly well worth reading, we may 

 mention the chapter on proportion, already described, and that on 

 regular polygons ; but besides these there are scattered up and down 

 the book many new or, at least, unusual demonstrations, and several 

 new constructions for the solution of problems. Moreover at the 

 end of each chapter are many well-chosen exercises, in all between 

 three and four hundred in number. In a word, Mr. Wright has 

 produced a work of considerable merit, which no one could study 

 from first to last without obtaining a thorough acquaintance with 

 the elements of plane geometry ; and as it is always instructive to 

 see the same thing from two points of view, a student who had 

 learned geometry from Euclid's ' Elements ' would doubtless learn 

 something from perusing it. 



We have hitherto spoken of the book simply with reference to its 

 contents. It has, however, a further claim on our attention ; for it 

 is expressly designed to supersede Euclid's ' Elements ' as a text-book. 

 In fact Professor Hirst mentions in his preface that it had its origin 

 in an experiment made by himself some years ago in the school con- 

 nected with University College, London ; and the experiment was that 

 of " teaching geometry instead of teaching Euclid." Now we are 

 perfectly certain that any class taught geometry by Professor Hirst 

 would be extremely well taught, and that at the least the usual per- 

 centage would leave the class with a sound knowledge of geometry 

 whatever the text-book used, or if, as seems to have been the case, 

 no printed text-book was used. Yet we think the antithesis hardly 

 just. The real subject of the experiment was whether Mr. Hirst 

 could teach geometry most conveniently by means of a manuscript of 

 his own composition, or by using Euclid's 'Elements of Geometry' as 

 a text-book ; and the question suggested by the present work is 

 whether, on the whole, it were better to use as a text-book of plane 

 geometry Euclid's 'Elements ' or Wright's 'Elements.' The question 

 is fairly raised in the present case, because it is unembarrassed 

 by the totally distinct question of alleged errors in treatment of 

 detail. 



Whether, as a matter of fact, Euclid's 'Elements' will be displaced 

 by a variety of text-books, some used in some schools, some in others, 

 we do not know ; but we must not disguise our opinion that the 



