QUICKEST DESCENT. 13 



Therefore, the descending body will not 

 oscillate on this curve. 



Cor. 6. If n be any point in the curve; then, 

 when » = 2, it is the least weight, that will 

 descend from A to », in the least time. 



SCHOLIUM. 



This Problem may be solved, in the fol- 

 lowing manner, by Euler's Theorem. 



LetP =-i:-:then,fluentrx=fluent^ ^{nz^-\-mp^) 





fluent\/ 



2>/^.^^( n X — m . V X* + y* ) 



= fJuentAX V V T-f- y x^ H-yQ .;^ 



Minimum, Woodhouse's Isoperimetrical Pro- 

 blems, page 51. 



But v = Ma;+Ny + P^: therefore, 



