2S8 Cambridge Coume of Mathematics. 



but to hail him as one of the immortals."* As a specimen 

 of rhetoric, this may be very fine, but we are persuaded 

 that its merit ends here. While a multitude of books, 

 which cost their authors much labor and reflection, are dai- 

 ly passing into oblivion, and while the whole volume of na- 

 ture lies open to our investigation, it is absurd to say that 

 any human work in any age, or in any department of learn- 

 ing, ever has or ever will put a period to the progress of 

 improvement, and arrive at perfection ; a state which van- 

 ity on the one hand, and enthusiasm on the other, have 

 dreamed of, but which the nature and destiny of human 

 things forbids us to expect ever to attain. Dr. Johnson 

 flattered himself for a while, he says, that his Dictionary, 

 which he had labored many years and with so much appli- 

 cation, would fix the English language, and put a stop to 

 those alterations which time and chance had before been 

 suffered to make in it without opposition, but he after- 

 wards found, that he had indulged expectations which nei- 

 ther reason nor experience could justify.! 



But to be more particular: we shall endeavor to shew. 

 that Euclid's Elements contain many imperfections which 

 are remedied in those of Legendre and Lacroix; and that 

 their Elements contain much valuable information which 

 will in vain be sought for in those of Euclid. Our remarks, 

 however, will be very brief, as it would be inconsistent 

 with our limits to enter into an extensive view of the sub- 

 ject. 



One particular in which the Elements of M. M. Legendre 

 and Lacroix are more valuable than those of Euclid, is, that 

 the latter treats the doctrine of ratios and proportion in B. 

 Vth as a separate branch of geometrical enquiry ; while the 

 former make the usual applications of this doctrine to geo- 

 metrical figures, without considering the demonstrations of 

 its principles as a subject belonging to geometrical investi- 

 gation. The demonstration of the first principles of the 

 theory of ratios and proportion belongs to arithmetic, and 

 its full developement to elementary algebra. It is because 

 most of us have learned this theory from Euclid, that we 

 are apt to imagine some almost necessary connection be- 

 tween it and geometry. This has been so much tfie case, 

 (hat Euclid's authority has been followed by almost all the 



*Edinb. Review, Vol. IV. p. 257. tPreface. 



