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

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47] FN and F L contrarily polited, that is, the ſhorter axis LF lying in the longer axis of the orbit A P, and the longer axis FN parallel to the ſhorter C Q. Let the focus of the laid ellipſis be in And ſuppoſe two other ellipſis L B I and L fl, to be drawn upon the common axis Ll, one paſſing 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 ellipſis LN I (which was similar to the orbit) in Q, the equant in p, and the ellipſis LB I (drawn through the interſection B,) in K. From the point K let fall KH perpendicular to the line of apſides QA P, and let it be produced ſtill it interject the Brit ellipſis LN/ in O, and the ellipſis L fl (paſſing through the focus f) in E. And laſtly, in the ellipſis LN/, let GM be an ordinate equal and parallel to EH. In which conſtruction it is to be noted, that the ellipſis L fl and LB/ are 'ſuppoſed 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 tranſverſe axis; and that E H or GM, the bale of the elliptic .ſegment GLM, ma?