15 8

Astronomy.

several Orbits of the Planets are laidin their proportional Distances

Plate

LVII.

Fig. 8.

Lib. I. Prop. XII, XIII.) therefore in the P ar(! K ]c$Velocity will be every where at P as a Perp erl V 1S Y let fall upon the Tangent P Y reciprocally*

(by Conies) S Y 2 : S P, and so S Y : */ P S : ^ etThe Velocity in the Parabola luill be every

V>‘

heft

or m

the Subduplicate Ratio

'f

</SP’

versely. \ ifl }

43. We have also shewn (Annot. XXXlV- iO'y ^Circle whose Radius is a, P = Periodical Titst e ’ y>

Velocity, that V P — a> an d V = —, and

P .» 1 .

a 1 a

~~ pz’ but also P 1 : a 3 , (ibid. II.) whence V 2: "s ’ 11

P

therefore V

: Z . Therefore the Velocity i

V)

i:i

a . #P

the Circle AG HI is to the Velocity in the Ch c 6

described with the Radius S P, as h_to

f

AS

/ 1 ;

J#

Buttb^^iofr

or V : v :: \/ S P : \A AS r V^L. ,cities in the Points A and P in the Parabola althe fame Ratio of \/ S P to \/\L (by 42*1 ’ A>'oquently, The Velocity in the Parabola at thefts asfithe Velocity in the Circlean the fame Difance A ’ QstVelocity in the Parabola at P is to the Velocity * n t^'described at thesame Distance S P ; that is , in the R awhere of %/ 2 to 1.

44. Again j the Velocity in the Circle who jju 5is | S P is to the Velocity in a Circle whose

S P, as \/ S P to \A ~S P, or as \/ 2 to I » , ^ $quently, The Velocity in the Parabola at P is e t liVelocity in a Circle whose Radius is § S P. » irifl&le

45. The angular Velocity of a Body P reV ? at £ '.any Orbit, that is, the Angle which is 5X13 Qcfy