164 HISTORY OF PHYSICAL ASTRONOMY. 



Newton allows that Hooke's assertions in 1679 

 gave occasion to his investigation on this point of 

 the theory. His demonstration is contained in the 

 second and third Sections of the Principia. He 

 first treats of the general law of central forces in 

 any curve ; and then, on account, as he states, of 

 the application to the motion of the heavenly 

 bodies, he treats of the case of force varying in- 

 versely as the square of the distance, in a more 

 diffuse manner. 



In this, as in the former portion of his discovery, 

 the two steps were, the proposing the heavenly 

 motions as a mechanical problem, and the solving 

 this problem. Borelli and Hooke had certainly 

 made the former step, with considerable distinct- 

 ness; but the mathematical solution required no 

 common inventive power. 



Newton seems to have been much ruffled by 

 Hooke's speaking slightly of the value of this second 

 step ; and is moved in return to deny Hooke's pre- 

 tensions with some asperity, and to assert his own. 

 He says, in a letter to Halley, " Borelli did some- 

 thing in it, and wrote modestly; he (Hooke) has 

 done nothing; and yet written in such a way as if 

 he knew and had sufficiently hinted all but what 

 remained to be determined by the drudgery of cal- 

 culations and observations ; excusing himself from 

 that labour by reason of his other business; whereas 

 he should rather have excused himself by reason of 

 his inability : for it is very plain, by his words, he 



