Mifcellanea Curiofa. 335 



(as will appear by dividing K-iVWV+—>—®^ 

 M«*.|>J r + L + 



v v 



V 



( fuppofmg the Progreflion - 

 to begin at r= 1.; That is V 

 (dividing all by % that fo , — 



the Progreflion may begin 



at!=± 0 JL = j: + JL , vv 



r m j^'^jf • r. rr 



+ ~+ ^,Thatis,inouc 1 v " 



prefent Cafe fbecaufe of 



&c. = — - — . That is, (putting n = m — ij — 

 m — i n 



of what it would have been if there had been no 



Refiftance. 



ii. This infinite Progreflion is fitly expref- 

 fed by an Ordinate in the Exterior Hyperbola, 

 parallel to one of the Afymptotes; and the 

 feveral Members of that, by the feveral Mem- 

 bers of this, cut in continual Proportion. As 

 is there demonflrated at Prop. 1 J. For let S U 9 

 (vid. Fig- 4. Tab. %.) be an Hyperbola be- 

 tween the Afymptotes A B, A F And let 

 the Ordinate D H (in the Exterior Hyperbola, 

 parallel to A F 9 ) reprefent the impreffed Force 

 undiminifhed ; or the Line to be deferibed in fad* 

 time, by a Celerity anlwerable to (uch undimi- 



oiftied Force. And let B S (a like Ordinate bei 



17% 



thereof - 3 which therefore, being lefi than D H 

 (as being equal to a Part of it) will farther 



*hat 



