( 573 )

1. Suppofe wc then the Force Impressed (and conscquently the Celerity,is thcre were no Resistance) as i ; the Resistance as r, (which must be lessthan the Force, or eile the Force would not prevail over the Impediment, tocreate a Motion.) And therefore the Effective Force at a first Moment , is tobe reputed as i — r That is, to much as the Force Impressed, is morethan the Impediment or Resistance.

5. Be it, as 1 — r to i,so 1 to m, ('which m is therefore greaterthan 1.)4.. And therefore the effective Force, (and consequently the Celer i ty) as-to a first Moment , is to be-of what it would be y had there been no»

m

Resistance.

c. This - is also the remaining Force aster such first Moment • and

m

this remaining Force is (for the fame realbn) to be proportionably abated

as to a Second Moment-: That is, we are to take- thereof, that is,

m

of the Impressed Force. And för a third Moment (at* equal Distancem m "

\ ‘m* :»*

!.. . .

of Time) —-for a fohrth — ; and so onwarddnfinitely.

m m mm +

6. Becausi the Lcngth dispatehed (in Equal Times) is* proportional tothe Cilcrities y the Lines of Motion *(anlwenng to thole Equal Times) are*

1 ,i 1 1

to be as-, —, -—-—, Ac. of what tbcy wonld have been in

m m 2 m 5 m 4

the sime Times, had there- been, no Resistance.

7. -Thiy therefore is a Geometrieal. Progression and (becaufe of m greaterthan r) continually Decreasing.

8. This Decreasing Progression Infinitely continued, (determining in thesime Point of Rest, where the Motion is-stipppföd to expire) is yet -of ' ti fi-»

nite Magnitude, and equal xo - os what it would have been ii*-,

m — I

much tirr>e* if there had been- no Resistance ; As is demonstrated in-my-Algebra , Chap. yy. Prop. 8. For (as I have eile where Demonstrated) the

A r . VR — A

Sttm or Aggregate 01 . a Geometrieal Pregreffion is-, ( fupposing- V

R — 1 tr “

thegreatest Term, A the least, and R the.Conimon Multlplier.). That is*.VR A _ ' .

rCT 7 — rZTI' Now Jn tlie P re ^ nt Lale, (lupposing the Progression

Infinitely