146

PI. LVI.Fig. 4.

Astronomy.

for that Reason called the Perihelion 'therefore, the Attraction of the Sun

strongs

6. For the Sun’s attracting Force being one

the Cause of the Planet’s Motion, and this For c ,® oiways increasing and decreasing in the inverse R al j' - { ythe Squares of the Distances, ’tis evident the Vp' 0 jpof the Planet will always be greater the nearer stthe Sun, and vice versa. Hence, the Motion of a ^net is every where unequable, being constantly &cC mLrated as it passes from A by D to P, and in the 0Half from P to A it is retarded. .

7. Yet is this unequal Motion of a Planet, reguss^by a certain immutable Law,.from which it never ^ ^which is, That a Line drawn from. the Centre of

to the Centre of the Planet does so move with the I q,about the Sun , that it describes elliptic. Areas ostusp s xtportional to the Times. That is, if when the * .

moves slowest it describes the Arch A a in a given f L jq'and when it moves quickest it.describes the Arch " hsthe fame Time, then will the trilineal Area A hequal to the other trilineal-Area ^ 8 P. . .

8. To demonstrate this., let the Time in whst

he'

...

vided into equal Parts,, and suppose that in the hr 11 a \\

Planet moves through the Periphery of its Orbit

it described any Right Line A B, by the P s0 J■ g p'Force in any Direction and the Centripetal F° rc .^jointly ; then in the second Part of Time itwouldceed in the same Right Line to c, if nothing p reV ? ^ ifso that B c — A B, as is manifest from the sirst ^Motion. - sf

9. Draw the Right Lines SB, Sr, and th 6 ,angles A B S and B c S will be equal, as havihfLBases AB, B c, and the fame Altitude of the ^1S. But when the Body comes to B, let the {os'

Force act with a new Impulse either equql to , qyolhmer or unequal, and let it cause the Body to declM 6 q ;the Right Line B c, and describe the Right Lut 6 j a 1draw C c parallel to B S, meeting B C in C j a ss. 6