Reeiew of O. Gregory^ Treatise on Mechanics. 8.3 



not one step is perceived by the mind ; of the latter, we 

 shall make some remarks before we close this review. 



Though the author's predilection for analytics, and ab- 

 struse theories, leads him far from that plain, and obvious 

 course, which is adapted to the understanding of learners, 

 there are nevertheless to be found some beautiful iliustra- 

 tions of principles, which serve to relieve the mind from the 

 tedium produced by intense application to abstract investi- 

 gations. Among these we would particularize that of 

 D'Alembertto show that the force is as the second fluxion 

 of the space divided by the square of the time, or in symbols, 



that F 0:4-- This, and the other fluxional formulae in va- 



riable motion are all founded on the 39th proposition of the 

 1st book of Newton's Principia, which as much transcends 

 all copies, and imitations of it, in elegance, as in the merit of 

 originality. It may have been, however, considered as too 

 abstruse for beginners. 



Other specimens of that kind of illustration, which tends 

 to illumine the mind of a student, and to advance the knowl- 

 edge of the sciences, may be found in Art. 230, 251, 328, 

 370,498, 532, and 417. 1 would select these as Scaliger 

 has some odes of Horace as preeminently beautiful, and as 

 forming a contrast to many others. 



The part of Chapter 2d, on the descents down inclined 

 planes, &ic. is an old subject, and has been repeatedly de- 

 monstrated, by the plainest principles of geometry, and 

 mechanics, and consequently established on the most cer- 

 tain foundation of human knowledge ; yet our author in 

 compliance with his own taste, or the fashion for analytics, 

 has thought fit to introduce a new set of demonstrations de- 

 pending on algebra, and the properties of goniometrical lines, 

 which are inferior in evidence to the propositions them- 

 selves, which were to be demonstrated. 



In Art. 277, we have the solution of the problem for find- 

 ing the curve of swiftest descent; the solution given by the 

 compiler is that of Thomas Simpson, but without any of the 

 necessary lemmatic principles, which are absolutely neces- 

 sary, for its logical, and mathematical conclusions. We 

 consider the whole, therefore, as useless, and nugatory, but 

 as compensated in some degree by the fine illustration?, 

 which follow. 



