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

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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 tranſverſe axis, is to the double of the tranſverſe axis.

  So that the ſector or triangle in orbits

nearly circular, is always nearly equal to the double of Bullialdus's equation.

  THE triangle and ſector being thus

determined, the equation for the tri- linear ſpace is accordingly determined. From what has been ſaid, it appears, that 1. THIS equation for the trilinear ſpace OKQ, is to that for the triangle OKF, in a ratio compounded of BN, the difference between the ſemi-tranſ- verſe and ſemi-latus rectum to the ſemi- latus rectum, and of the duplicate pro- portion of the ſine OH to the radius ; or OKQ is to OKF, in a proportion compounded of the duplicate propor- tion of the diſtance of the foci to the ſquare of the leſſer 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 conſequently it holds in this proportion to the double of Bulli- aldus's equation. 2. THIS