70 Notices respecting New Books. 



student's feelings, and confusion in his comprehension and remem- 

 brance of the argument. One attempt to remedy this inconvenience 

 was made by Mr. Williamson in his " Symbolical Euclid," Avhich 

 was in a great degree successful as far as this particular class of dif- 

 ficulties was concerned : but on the other hand it was attended with 

 incalculable injury, by removing from geometry that distinctness of 

 conception, both as regards fundamental ideas and the nature of geo- 

 metrical demonstration, which has from time immemorial been the 

 peculiar charm and value of this science. Mr. Potts, however, has 

 literally maintained the very text of Simson and secured the very 

 spirit of Euclid's geometry, by means which are simply mechanical. 

 It consists in printing the syllogism in a separate paragi-aph, and the 

 members of it in separate subdivisions, each, for the most part, occu- 

 pying a single line. The divisions of a proposition are therefore seen 

 at once without requiring an instant's thought. Were this the 

 only advantage of Mr. Potts's edition, the great convenience which 

 it affords in tuition would give it a claim to become the geometrical 

 text-book of England. This, however, is not its only merit. 



Prefixed to the work is an elaborate history of geometry, — too 

 elaborate in respect to the early geometry, perhaps, and too sketchy ■ 

 in respect to the modern. In its general character it resembles the 

 prefaces of Bonnycastle and Butler, but is in many parts much more 

 amplified than either. We would recommend the author to recast 

 this in a second edition — to omit some of the details respecting 

 mediaeval geometry, and to give an ample analysis of the researches 

 of the continental geometers of the last half-century. This part of the 

 work, indeed, satisfies us less than any other ; although it is not 

 without considerable merit. 



The " notes " appended to each book of Euclid in succession (and 

 a few additional ones in the " Appendix ") are partly critical as re- 

 gards turns and expressions in the original text of Euclid, but prin- 

 cipally geometrical as regards difficulties of conception or imperfec- 

 tions of demonstration. They bespeak an acute mind and a judi- 

 cious teacher ; and they will be of very great service to the solitary 

 student and careful thinker. 



Then follows a dissertation on the "Ancient Geometrical Analysis," 

 somewhat incomplete it is true ; the subject is, however, resumed in 

 the " Appendix," and treated with a fulness and perspicuity that is 

 very unusual (perhaps unprecedented) in treatises even professedly 

 composed on the subject — such as those of Lawson and Leslie. This, 

 with the judiciously chosen illustrations of the method, cannot fail, 

 we think, in reviving amongst Cambridge men a taste for that most 

 interesting department of the Greek geometry ; and, if not amongst 

 the older members of the University, yet amongst its coming race 

 of men, from the facility and ease with which Mr. Potts has put it in 

 their power to master both the method and its application, this sub- 

 ject will regain something of the respect which was paid to it in the 

 bygone brightest days of geometry. 



In the "Appendix" is inserted a short tract on the "Theory of 

 Transversals" — a subject almost totally unknown in this country. 



