i55

Astronomy.

k,.- 1 an< ^ gives a iust Idea of the Number ,

vZlQtl? s\ J J

’ ^rder^ and Positions of the heavenly

Bodies :

Q *' ln fin'

- t ^ len the Curve or Trajectory will becometn , ne A C : or the Projectile will descend di-

*,!i r« A C '” trc of Force c '

: the Area of any Ellipse, S, S, s, the

p ~ ■

V r > b th he 4 ector ? A S B, B'S C, C S D, & c . and

f e hay^ q 6 ^'nies in which they are described ; then‘ r 5 y trv :: T : T, and S : s :: T : t, and so on

. ' I' ■. n ^ctor through the whole Area. Therefores<r ‘ Su ^ ~h 5: T + T-j- t ” Sum of all the Sec-,b s tl\ e "‘ of all the Times in which they are described ;^°le v "vie Area A to the periodical Time P os a9fyj £ C ^°^Son. Consequently, S X P — T X A,

and in a given Particle of Time T,

av e p as A

S*

3s. tz

i- qq 25 . we have the principal Lotus Rectum

rs ’ hut in a given Time the centripetal Forcey is - I

** ib. Sj3I j Wherefore in a given Time L : QT* X

y r 0

scf ib». . 0 Lf : QT X S P : S, the Sector A S B de-

v( * in a • A

4-n Aven Time. Whence P : ^- 7 ; therefore

fb' c ^ x •* J 2

K L,^ u PlicQjL J^at is, The Area of an Ellipse is in the

<! »i.

n . -j — - rj- ~~r

Cr koL f' att0 of the Latus Rectum and Periodical

36.

&5te ™o\v _ . „

> th en ., et a = Transverse Axis, and b — Conju-

^ z - C? C° n ics) a : b :: b : L,' and so b z = a L,a % * M

th,

:atl gle

whence a

X L z . But the

°re

® X Z> ; A, the Area of the Ellipse (by Conks)

sti X l*.

:P.

A : P X L’ (by Article 35 .) that

or j The Periodical Time is in the Sejqui-

plicate

PlateLVII.Fig. 4 .