INTRODUCTION. XXV11 



subject and of the Book, as can be attained by a 

 moderate degree of labour, and an acquaintance 

 with only elementary mathematics. 



II. The accomplishment of the other object of 

 this Treatise, examining the connexion of the dif 

 ferent parts of the Principia with each other, and 

 with former and subsequent discoveries, showing its 

 transcendent merits, and removing the objections, 

 or rather the criticisms, that have sometimes been 

 offered upon a few comparatively unimportant por 

 tions of the great work, will, beside performing 

 that service, also afford additional help to the study 

 of it, and tend to promote the taste for understand 

 ing it, so as to judge of its unparalleled excellence. 

 It is satisfactory to find that many of the propo 

 sitions are capable of demonstration by a process 

 different from that employed by Newton, especially 

 when this process is more easily followed. In 

 many cases the analytical substituted for the syn 

 thetical method, is interesting as a matter of curi 

 osity, independently of its more didactic character. 

 This may also be predicated of the occasional pre 

 ference of algebraical to geometrical reasoning. 

 The greatest interest, however, belongs to observ 

 ing the mutual bearings of the propositions, per 

 ceiving sometimes how one arises out of another, 

 sometimes how the two are so connected that toge 

 ther they exhaust the subject, sometimes how the 



