>53

Astronomy.

be looked upon as circular ,

-VJ XKJKJ JWV.t U. jJ'JLl CKkJ Ketet ^ vvr-r, j

3g ra as represented in Orreries and Di-riS ’ without any sensible Error,

Sj».

i.Q.T l

The

Therefore the centripetal Force is as

it v , nve rfely ; 0 r, because L is a given Quantity,

‘ he Erectly as _l_

?6 j ^ as S p*‘

?|j!ch now shew what Ratio the projectile Force

L S\ fsœ ES- a t0 describe a Circle has to that

^ paribtts) causes the Body to describe anyjiH ' .^ot us astume this Ratio to be that of n

A te |y P ut ting 2 a and 2 b for the transverse and con- Platet Jg A j?' etc rs of the Conic Section A N, the Circle LVIE4 s to its if su PP° se the right Line EF to move pa- Fig, 2 ,of ? L^ e th n an< ^ the Points a and d therein so as toat Li 6 Lurv es A I and A N ; and let the Distances e L°m AB be call’d x, viz. AE=#;. and7.-1 •. tr the Diameter of the Circle.

-xx

E d in the Circle, and *L.\r* X

^ ** = E a in the Conic Section. The Fluxions

lC0r din;nw r , , r . d—xX*a . tes L d and E«, vi%. — 7—r —z^d

AIT.

A

l 4s c t sie Cu rves in the Direction E F or ^ B. But

V — y If (I —j- #

U3c ‘0ns are as —— and - X ---

\/ a dx—rxxr, will be as the Velocities in every

■‘Wdi

Ar, V'

2 d — x ' a 2 a- + x

* \

, - ] and therefore when E F arrives to

ivy, ' a > the Ratio of those Fluxions or Velocities

Cc °ttie tW r d h a

e that of --to —X —7-=, or as y/ £

V id

" %/ 2(1

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