Notices respecting New Boohs. 71 



and little need be added to the notice already given in this Magazine 

 (see vol. xxxii. S. 3. p. 69), beyond the assurance that the new edition 

 possesses all the best and most characteristic features of the old one, 

 minus many of its imperfections. The conscientious care with which 

 the verbal defects of Simson's text have been emended cannot be too 

 highly praised, and it must be a great satisfaction to Mr. Potts to 

 know that he has done much towards the cultivation, in our schools, 

 of a more correct taste, as far as the purity of geometrical reasoning 

 is concerned. In fact, if we were to judge the work merely from its 

 author's own point of view, that is to say, as a careful reproduction 

 of, and judicious commentary upon the 'Elements of Euclid,' we 

 should have little to say except in praise of the result as now offered 

 to the public. It is only when we take different, and higher ground, 

 when, in short, we compare this treatise on the science of geometry 

 with the purely ideal one which English students do not, but ought 

 to possess, that we find room for much criticism. 



We have no desire to enter here into the question epineuse as to 

 the absolute merits of Euclid's ■ Elements ; ' as a classical work it is 

 second to none in point of interest, and it will ever continue to be 

 studied by men of culture. The opinion is gaining ground, however, 

 that our national admiration of Euclid has been carried too far — that 

 it has too long deprived our schools of the advantages to be gained 

 from an elementary treatise on geometry which, although based upon 

 the old one, shall be superior to it in point of method and accuracy, 

 of purely English origin, and in every way worthy of the present 

 state of the science. Even in our universities, which are proverbially 

 and, on the whole, wisely conservative, symptoms of a more vigorous 

 and healthy criticism — too long discouraged by an inordinate notion 

 of Euclid's perfection — manifest themselves more and more frequently. 

 Mr. Potts' notes to the several books of Euclid might be cited in sup- 

 port of our assertion, whilst the frequent use in them of such words 

 as seems and appears, in place of the more decisive and emphatic verb 

 is, curiously enough indicates the state of transition to which we 

 have referred. Numerous instances might be given ; let one suffice. 

 In his notes to the 3rd book, Mr. Potts modestly informs us that 

 the 9th proposition " appears to follow as a corollary from the 7th," 

 whereas it is, as he well knows, a purely logical consequence of the 

 latter ; for if it be impossible to draw more than two equal lines 

 from any non-central point to the circumference of a circle, any 

 competent logician, even if he were ignorant of the very nature of a 

 circle, would be able to conclude that the point must be a central one 

 from which three equal lines can be drawn to the circumference. 



Having mentioned these notes, it is but just to add that in their 

 present improved form they constitute a very valuable feature of the 

 work, and on the whole are both judicious and accurate. Whilst 

 admitting, however, that the opposite excess would have been in- 

 tolerable, we cannot but think that the notes in question would have 

 been of far greater value had they been less purely explanatory, and 

 more thoroughly critical. Instead of " exemplifying " by geometrical 

 figures such axioms as ,; if equals be added to equals the wholes are 



