47 



the process would have been veiy intricate, and it would 

 have been difficult to have obtained the conclusion required. 

 This makes it bighly probable, that Newton himself disco- 

 vered the precise error; and, on account of the subsequent 

 difficulty, abandoned this mode of solution for that which he 

 afterwards gave. 



The Newtonian solution is here given in the words of the 

 author, as well as two of the solutions of Lagrange. This 

 seemed necessary for making intelligible the remarks on 

 these solutions. This paper concludes with a solution de- 

 duced entirely from the method of limits and series. 



d c B D K 



" Prob.* Tendat uniformis vis gravitatis directe ad pla- 

 " num horizontis, sitque resistentia ut medii densitas et 

 " quadratum velocitatis conjunctim: requiritur tuni medii 

 " densitas in locis singulis, quae faciat ut corpus in data 

 " quavis linea curva moveatur, tum corporis velocitas in 

 " iisdem locis. 



" Sife 



* Edit. Prin. 1687, pag. 260. 



