tha Force imprelTed, is more than the Impediment or Re- 
fiftance. 
5. Be it as i— rto i ; fo i tow. ( which m is there* 
fore greater than i.) 
6. And therefore the efFe£tive Force (and confequent- 
ly the Celerity ) as to a firft Moment, is to be «^k)f what 
itw^ouldbe, had there been no refiftance. 
7. This w is alfo the remaining Force after fuch firft 
Moment ; and this remaining Force is ( for the fame Rea-» 
Ibn ) to be proportionally abated as to a fecond Moment : 
1. ± 
that is we are to take m thereof,that is mm of the imprelTed 
Force. And for a third Moment ( at equal diftance of 
i. i. 
time) mmm ; for a fourth ; and fo onward infinitely. 
8. Becaufe the length difpatched ( in equal times) is 
proportional to the Celerities ; the Lines of Motion ( an- 
i i i i. 
fwering to thofe equal Times )are to be as m^ m^, m^^m^^ 
&c, of what they would have been, in the fame Times, 
had there been no refiftance. 
9. This therefore is a Geometrical Progreffion ; and 
( becaufe of m greater than i ) continually decreafing. 
10. This decreafing ProgrefTion infinitely continued 
( determining in the iame point of Reft, where the Mo- 
tion is fuppofed to expire) is yet of a Finite Magnitude ; 
and equal to m—x of what it would have been in io much 
Time, if there had been no refiftance. As is demonftra- 
ted in my Algebra, Cha^, 95. 'Prof. 8. For (as I haveelfe- 
where demonftrated) the Sum or Aggregate of a Geome- 
trical Progreilion is-^^—Y' ( fiippofing V the greateft 
term, A the leaft, and R the common multiplyer.) 
That is — • Now in the prefent Cafe, ( fiippo- 
ling the Progreffion infinitely continued) the leaft term 
be- 
