Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/129

 Rh

Of the motion of bodies in eccentric conic ections.

If a body revolves in a ellipis: it is required to find the law of centripetal force tending to the focus of the ellipis. Pl. 4. Fig. 2.

Let S be the focus of the ellipis. Draw SP cutting the diameter DK of the ellipis in E, and the ordinate Qv in x; and compleat the parallelogram QxPR. It is evident than EP, is equal to the greater emi-axis AC: for drawing HI from the other focus H of the ellipis parallel to EC, becaue CS, CH are equal ES, EI will be alo equal, o that EP is the half um of PS, PI that is, (becaue of the parallels HI, PR, and the equal angles IPR, HPZ) of PS, PH, which taken together are equal to the whole axis 2AC. Draw QT perpendicular to SP, and putting L for the principal latus rectum of the ellipis (or for $$\scriptstyle \frac {2BC^2}{AC}$$) we hall have L × QR to Rh