Astronomy.

r though the Planetary Orbits area v elliptical, yet is the Eccentricity C S,

in

'^et-y a Body revolve in an Ellipsis A P Q_, by a ForceZ ail/ ere d'.refl ed to the Centre C ; it is required to findfee Tan ^ lat F°rce. Let Q y be drawn parallel toPar a ]iei P R, and PF perpendicular to KC; and^tried - r ,° " F join C Q : the rest as before. The right-

An c i rr —' ~~~

3n gle * P C is e( l ual t0 twice the T ri '

^Porti^ i w ^ich is a constant Quantity, as being11 ' s des 0 -! t0 constant Particle of Time in which•"°*'ftant- < r\k e< L Also in the Ellipsis D K X P F is a

tant

fe^’FxPC'

iS fe o'^antity (p e r Conies). Therefore DICXPF°r Qjn X P F, that is, D K to Qjn,

^^'Psi? Cl1 wherever the Point P is taken in the

to Q ju 1

is a

ipr* I,

>lfani Hen ce also the Ratio of D K10 X Jn ne ' Fut in the Ellipsis D K*; Qju 1 :: P G .j^d thg rys/^ r Conies.) Now because (fy Q_R,.feall ,, Terence between G v and G P is infinitelya ' sier e f ore P-v X <nG - QR XPG; whence PG 1f c ^°. nstant Ratio to P G X QK, that is, QJR or” 0 s eta l Force is every where in a constant Ratio to2z. F C, the Distance from the Centre.off t ence if the Centre C of the Ellipsis were toC ^tig E( j 0 . an infinite Distance, the Ellipsis would be?^e, a n j nt |° ^ Parabola , in which the Body wouldrjfee t “ e P orce now tending to a Centre at an in-^. nCe ^ould become equable, or the same with

G;

• . «inu Ln,CU»i‘ v v 'i *

thep^' according to the Theory of G*™*’ theB 0( i ara boh should be changed into an Hyp ’

.ft””'" ~~ » .hat Carve by <t» fffZZ° fCe now changed from a centnpeta

thp r , Qste 5 because now it causes the Body to rfeefttre.

ady to recede from

0f, ce Let it be required to find the Law of the

<"-!» .

Foc?f *o 0ne °f ^ 3e Foci of an Ellipsis. Draw S Ps d, and PH to the Focus H, and HI pa-ls, 4 rallel

i-5X

PI. LVLFig. 8.

PI. LYII.Fig. i.