1.56

PlateLVII.Fig- 5 -

Astrono m y.

Bodies: But the Proportion of

&

and Dijiances of the Planets is not to o^ £j J

t¥

■plicate Ratio of the Transverse or greater ■^ ><tSEllipse.

37 - Hence the Periodical Time will be the j, t o 5all the Species of an Ellipsis from a Right L 11 ^,, ofCircle described upon the same transverse D:an lCmore particularly, the Time of describing d^ eEllipse AED will be the same as that of t,,e j <l cEllipse A O D ; and the same also as the Ti 01 ® Sp s 'scribing the Semi-Circle A P D, which is only 0 v>cies of an Ellipsis, where the Foci coincide z tilCentre N, and the Semi-Conjugate N O bees j-jjjplSemi-Diameter N P. Lastly, when theA O D degenerates into a Right Line A D bying the Semi-Conjugate N O in injjnitum, aI r j s pi 5 ".cus receding to the End of the Axis at IT lt , fotflthe Time of describing the Line A D is st*H l> Sj>,

38. The Velocity of the revolving Body P iS 2

S Y being a Perpendicular let fall on the j 5 es,from the Centre of Force S ; for the VelosiiT^ Pjas the small Arch Q_P described in a given JeQJ 3 — PR, in its evanescent State : And ppl ,the Right Angles at T and Y, and the Angl e ~j .YP S when the Points Q_, P, coincide, the c . ^ C ( c °aTriangle QP T will be similar to P S Y ; an fgive Q_P (—PR): Q_T P S : S Y ; whe* c

SPXQ.T ciivoT.Tsi thereso^

SY

But S P X Q.T : Lt 3

That is, The Velocity is in the Su,

■bduf c0tl

P 1 ' 1 '

n>

’f

S Y* * ' “"“ v " ~ ' r lcU W

of the Latus Rectum directly, and the P er f cn A

39. Hence the Velocities in .the greatei j o> jDistances A and D are in the Ratio cornp° ul1 'pist®* 1