perpendicular deſcent, deſcribes the line CB. Q. E. I.
Case 3. And by the like argument if the figure RPB is a parabola, (Fig. 3.) and to the ſame principal vertex B another parabola BED is deſcribed, that may always remain given while the former parabola in whoſe perimeter the body P moves, by having its latus rectum diminiſhed and reduced to nothing, comes to coincide with the line CB; the ſegment BDEB will be proportional to the time in which that body P or C will deſcend to the centre S or B. Q. E. I.
Proposition XXXIII. Theorem IX.
The things above found being ſuppoſed, I ſay, that the velocity of a body in any place C is to the veolocity of a body, deſcribing a circle about the centre B at the diſtance BC, in the ſubduplicate ratio of AC , the diſtance of the body from the remoter vertex A of the circle or rectangular hyperbola, to , the principal ſemi-diameter of the figure. Pl. 15. Fig. 4.
Let AB the common diameter of both figures RPB, DEB be biſected in O; and draw the right line PT that may touch the figure RPB in P, and likewiſe cut that common diameter AB (produced, if need be) in T; and let SY be perpendicular to this line. and BQ to this diameter,
