Mifcellemea Curio f % . 163 



pos'd conftant every where in this Calculus) 

 and consequently BG 2 tidx 2 dy 2 , whence 

 ydx 



a conftant Quantity. Let & 



dxdx~\-dydy 2 



be any conftant Quantity, and confequent- 

 ly (to obferve the Law of Homogeneals) we 

 ydx a 



have s= — 9 as has been found 



dxdx -\- dydy 2 dy 3 



by the Uluftrious V Hofptall^ and the cele- 

 brated Jo. Bernoulli, 



PR OB. II, 



To fnd the Line of Swiftefl Defcent, 

 (Fig. 25.; 



Let BC, CD, be two infinitely fmall Par- 

 ticles in the Curve fought. Now this Curve 

 ought to be of fuch a Nature, that, fuppo- 

 fing a Body to have fallen from the Hori- 

 zontal Line AQ, it may pafs from B to D 

 in the jhorteft Time. Therefore we are to 

 find out the Point C (in the Line RS drawn 

 in fuch a manner parallel to AQ., that the 

 differences of the Ordinates GC, DE, may 

 be equal) fuch that this may ' come to 

 pafs. 



Now the Velocity in C is VLC, and that 



BC 



in D is VQP h therefore — — is the Time 

 M a of 



