A

STRONG M Y.

lri ^ r °® ^ ie Orrery, but by Delineation,

tr.

Whijh.

h^fe L S . S A a nd S-D. inversely, in the same Fi

*1 . ^ *1 ['"I VPT1 i /lufitir • bp/'mi Cr* i n *.1, _ /*,

J lst;

i +0,

0. 'Ri are the Perpendiculars.W n r f fore if a Circle D I

«ie,

cit/^ v

as . v/ L to %/” 2 D S

*57

on 's Solar System ; where the

several

*n Ces a s :vcn Quantity; because in that Case the

E C F be described at

of El]; *^ ance S D, because the Circle is that 8pe-

7 j\‘P‘ iS whose Lotus ReSiuni is equal to the Dia--- M -

,'Qdv; nc e

4(,

t-k rL-"~ * u,1 “- J -' io “* "

,Ug e Circle in the Subdimlicate Ratio of L toh e n > or .

biE ^ , and f-nce in this Point D the perpendicu-i n , ce is the fame in both, the Velocity of thee Ellipsis at the Point D is to that ot a body

and the fame mayto the Velocities at the other

: ^ Wl th respect

w . •j.

t; p 11 bi{n C ° m pa re the Velocity in the Ellipse at theS I at the c Ce ® w 'th that of a Body describing a CircleR Distance C B from the common Focus

t 0 a f > RT^dius of the Circle r AC = CDrSB,set E*erts~ . e r Semi-Axis B C, which is here equalt). tn e y^dicular S Y to the Tangent in the Point B.,v a N(j e <*% in the Ellipse be V, and in the Circle>, of S 1 ^ Lotus Return of the Ellipse, so 2 A"g*. "Tys Circle ; therefore (Art. 3.8.) V ; f u

E lt ' V’ °r V 1 : :: ~ • f :: L X A : 2 B

2 b B A 1

1 'c 4 (Ey Conies) A : B :: 2 B ; L, therefore;^ E ; conseauentlv V 1 = v\ and so V = v.

F

ate

VII.

ig- 6.

f'k,sr et v r' '

Thr’ con sequcntly V x *—v ,li { s j€ Priority of the Body in the Ellipse In the^Qn to that in the Circle E F described with

V^.It^WrSB.

• 'been _ /i_ / a..* > fi-n*-

11 ‘ac yofa Bodt

t0, ‘“Mt;

w •. A n Y ‘-ame Distance from tire focus, as 2fcSs tl >cause every

already (hewn (Art. 29.) that thsy in the Vertex of a Parabola is to thatT at the same Distance from the Focus, as \/d because every thing that has been shewntde lotion in an Ellipse may I.e demon-° os t ^Raraboh and Hyperbola, (See Frwcip.

Lib.

Fie. 7-