I

- ( n «)

lö.Becaufc FL, LM, MN,& areas

r i i , .

--, —-» &c. fln-

m m m «)

finitely) Terminated at A ; thercfore (by Prop. 8.) their Aggregate F A,or d /?, is to D H, (so much Lengtli as would have been di/patched in thefame Time, by iiich Impreiled Force Undiminished) as i to m — i —

17. lf therefore we take, as 1 to n, io AF ty D H; this will repreienrthe Length to be Diipatched, in the fame Time, by such UndiminishedForce.

18. And if such D H, be suppo sed to be. Divided into EquaJ Parts In-numerable (and therefore Infinitely finali;) theie anfwcr to thole (as many)iParts Unequal in F A, or h d.

19. But, what is the Proportion of r to 1, or (which depends on if)of 1 — r to 1, or 1 to r» j remains to be cnquired by Experiment.

2.0. If the Progression be not Infinitely Continucd; but End (siippofe)

V i

»at N, and its leastTerm be A —. M N : then outof - — - -F

R — I m

■, (as at Prop. 8.) that is,

-F Gc. That is, (in our

1

m 3

, (as by Division will appear)

Gc. is to be Subducted

A

R— 1A A

R* ^ R3

present Laie)

m m

m

-F Gc. And»io the Aggregate will be

1 — a

m m

I — a , 1

-h Gc.— —

m 3

And thus asto the Line of Projectiori , in which (Secluding iht P^sistance)the Motion is reputed Uniform ;-di(patching Equal Lengths-at Equal Times.Consider we-next the Line of Descent.

xi. In the Dcseent of Heavy Bodies, it is iiippoied, that to each Moment. j of Time, there is iuperadded a new Impulse ot Gravity to what was before :

j j And cach of theie, Secluding the Consideration of the Aia Resistance, to pro-

III .Iceed equally (from their icveral beginnings) through the iucceeding Mo-I I I I ments. As, (in the Erect Lines) I I I I Gc. III Gc. I I Gc. I Gc.iö continually, as in the Line of Projectiori.xx. Henceariieth (in the Traniverse Lines) for the first Moment 1,for the iecond 1 -t- 1, for the third 1 *F l -F 1, and so forth in AritbmcticalProgression. As are the Ordinata m a Triangle at Equal Distance.

xz. And iiich are the continual Increments of the Diameter, er of theOrdinate s in the Exterior Parabola , aniwcring to the interior Ordinata , orSegments of the Tangent , equally Incrcasing ; As is known, and commonlyadmitted.

^4. If