354 Miftalknea Cwiafa. 



8. Becaufe the length dilpatched (in equal 

 times) is proportional to the Celerities ; the Lines 

 of Motion (anlwering to thofe equal Times) are 



to be as -i, -i-, -i, &c* of what they 

 m m tn m 



would have been, in the fame Times, had there 

 been no Refiftance. 



9* This therefore is a Geometrical Progrefli- 

 on ; and (becaufe of m greater than i) cotinual- 

 jy decreafing. 



io~. This decreafing Progreffion infinitely 

 continued (determining in the lame Point of 

 Reft, where the Motion is fuppofed to ex- 

 pire) is yet of a finite Magnitude 7 and equaj 



t 0 — , of what it would have been in (b 

 m — i 



much Time, if there had been no Refiftance. 

 As is demonftrated in my Algebra, Chap. 95-. 

 Prop. 8. For (as I have elfewhere demonftra- 

 ted) the Sum or Aggregate of a Geometri- 

 cal Progreffion is V ^~~ A ( fuppofing V the 

 Hr- * 



greateft Term, A the leaft, and the com- 



mon Multiplier. ) That is - — — - ' 



r ' ' It— 1 ^ — 1 



Now in the prefent Cafe, (fiippofing the Pro- 

 greffion infinitely continued) the leaft Term 

 A, becomes infinitely finall , or = o. And 

 A 



confequently- doth alio vanifli, and there- 



by the Aggregate become, 5 j£^ c ^at ** 



