Chap. i. PHILOSOPHY. 165

greatest distance to the least is something lest, than the propor-h°n of 9 to 8; but much nearer to this, than to the propor-hon of 10 to 9. In Jupiter this proportion is a little greater,than that of 11 to io. In Mars it exceeds the proportion of6 to y. j n the earth it is about the proportion of 3 o to 29.■hr Venus it is near to that of 70 to 69. And in Mercury itc °nies not a great deal short of the proportion of 3 to 2.

7 * E a c h of these planets so moves through its ellipsis, thatbile drawn from the fun to the planet, by accompanyingae planet in its motion, will describe about the fun equal fpa-Ces in equal times, after the manner spoke of in the chapter ofc ^tripetal forces a . There is also a certain relation between

e greater axis’s of these elliplis’s, and the times, in whiche planets perform their revolutions through them. Whichre Wion may be expressed thus. Let the period°ne planet be denoted by the letter A, thej^ c ater axis of its orbit by D; let the periodMother planet be denoted by B, and thejjf e ater axis of this planet’s orbit by E. Then

be taken to bear the fame proportion to B, 7

b bears to A; likewise if F be taken to bear the fame pro-f° r tion to E, as E bears to D : and G taken to bear the seme

Dl7\ . 7

^ portion likewise to F, as E bears to D; then A shall beare fame proportion to C, as D bears to G.

O rp ^

. ' J- he secondary planets move round their respectivear 7> much in the seme manner as the primary do round'

the

A DB EC FG

Mm

* Book I, Ch. J. § 29.