Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/228

 perpendicular decent, decribes the line CB. Q. E. I.

. And by the like argument if the figure RPB is a parabola, (Fig. 3.) and to the ame principal vertex B another parabola BED is decribed, that may always remain given while the former parabola in whoe perimeter the body P moves, by having its latus rectum diminihed and reduced to nothing, comes to coincide with the line CB; the egment BDEB will be proportional to the time in which that body P or C will decend to the centre S or B. Q. E. I.

The things above found being uppoed, I ay, that the velocity of a body in any place C is to the veolocity of a body, decribing a circle about the centre B at the ditance BC, in the ubduplicate ratio of AC, the ditance of the body from the remoter vertex A of the circle or rectangular hyperbola, to $$\scriptstyle \frac 12AB$$, the principal emi-diameter of the figure. Pl. 15. Fig. 4.

Let AB the common diameter of both figures RPB, DEB be biected in O; and draw the right line PT that may touch the figure RPB in P, and likewie cut that common diameter AB (produced, if need be) in T; and let SY be perpendicular to this line. and BQ to this diameter,