Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 2.djvu/511

 47] FN and F L contrarily polited, that is, the horter axis LF lying in the longer axis of the orbit A P, and the longer axis FN parallel to the horter C Q. Let the focus of the laid ellipis be in And uppoe two other ellipis L B I and L fl, to be drawn upon the common axis Ll, one paing through the point B, where the perpendicular FN interjects the orbit, and the other through the focus  Let the line FR, revolving with the planet in the orbit, be indefinitely produced, till it interject the f1r{'c ellipis LN I (which was similar to the orbit) in Q, the equant in p, and the ellipis LB I (drawn through the interection B,) in K. From the point K let fall KH perpendicular to the line of apides QA P, and let it be produced till it interject the Brit ellipis LN/ in O, and the ellipis L fl (paing through the focus f) in E. And latly, in the ellipis LN/, let GM be an ordinate equal and parallel to EH. In which contruction it is to be noted, that the ellipis L fl and LB/ are 'uppoed as drawn only to divide the line OKH in given proportions, that KH may be to UH, as the latus rectum of the orbit to the tranvere axis; and that E H or GM, the bale of the elliptic .egment GLM, ma?