INTRODUCTION. 



acquainted with the discoveries of Newton, and the 

 history of the science, but without examining the 

 reasoning, and those who would follow the reasoning 

 to a certain extent, and so far as a knowledge of 

 the most elementary parts of geometrical and ana 

 lytical science may enable them to go. It has 

 been found upon trial that readers of both descrip 

 tions have been able to peruse the work with 

 advantage, even readers of the second description. 

 These have easily followed, not only the commen 

 tary upon the gradual progress of discovery, and 

 the state of the science before Xewton*, but passing 

 over the exposition of the differential calculus f 

 have pursued the demonstration of the fundamental 

 law of gravitation J, and even apprehended the 

 proof of its universal action according to the inverse 

 proportion of the squares of the distances. Pass 

 ing over the detailed discussion of central forces ||, 

 the illustration of its application to planets and 

 comets is involved in little difficulty ^f; and the 

 manner of finding the place of these bodies at 

 given periods of their revolution may be under 

 stood without entering into the details of the in 

 vestigation.** The ascertainment of the force 



* First 20 pages. f P. 20. to p. 31. 



J P. 31. to 41. P. 41. to 50. 



II P. 50. to 64. [ P. 64. to 69. 



**P. 69. to 76. 



a3 



