Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 2.djvu/520

            [ 56 ] ratio. But this triangle OFK, when at a maximum, makes an angle of mean motion, which is to the angle called R, as BN, half the difference between the latus rectum and tranvere axis, is to the double of the tranvere axis. So that the ector or triangle in orbits nearly circular, is always nearly equal to the double of Bullialdus's equation. THE triangle and ector being thus determined, the equation for the tri- linear pace is accordingly determined. From what has been aid, it appears, that 1. THIS equation for the trilinear pace OKQ, is to that for the triangle OKF, in a ratio compounded of BN, the difference between the emi-tran- vere and emi-latus rectum to the emi- latus rectum, and of the duplicate pro- portion of the ine OH to the radius ; or OKQ is to OKF, in a proportion compounded of the duplicate propor- tion of the ditance of the foci to the quare of the leer axis, and the dupli- cate proportion of the line OH to the radius. For the trilinear figure OKQ and the triangle OKF, are nearly as OK and KH, which are in that pro- portion, and conequently it holds in this proportion to the double of Bulli- aldus's equation. 2. THIS