XX INTRODUCTION. 



many steps in the process.* But it is equally un 

 deniable that with very moderate mathematical 

 acquirements, a distinct and accurate knowledge 

 may be obtained of the fundamental truths un 

 folded, of the reasoning by which some of them, 

 and these the most important, are sustained, and 

 of the nature of the proof on which the others rest. 

 There is not much difficulty, indeed, in learning 

 those truths, in comprehending the propositions 

 without going further. But this is in every way 

 a most imperfect knowledge, and neither can give 

 satisfaction though retained, nor is likely to be re 

 tained without a knowledge also of the demonstra 

 tions. A great advantage, however, is gained, if 

 the learner can not only follow the demonstration of 

 the more important propositions, so as to be satis 

 fied of their truth, but can comprehend the nature 

 of the proof in the other instances. He has both 

 made solid progress in mastering the principles of 

 the science, and has become able to judge for 

 himself the merits of the great work which first 

 taught it to the world. 



Thus two classes of readers may benefit by this 

 Analytical View ; those who only desire to become 



* No one needs scruple to confess how difficult he has found the reading 

 of the Principia, when so consummate a geometrician as Clairaut has made 

 a like observation, (Mem. Acad. 1745, p. 329.), though somewhat qualified. 



