Section VI.
How the motions are to be found in given orbits.
Proposition XXX. Problem XXII.
To find at any aſſigned time the place of a body moving in a given parabolic trajectory.
Let S (Pl. 14. Fig. 1.) be the focus, and A the principal vertex of the parabola; and ſuppoſe 4ASxM equal to the parabolic area to be cut off APS, which either was deſcribed by the radius SP, ſince the bodies departure from the vertex, or is to be deſcribed thereby before its arrival there. Now the quantity of that area to be cut of is known from the time which is proportional to it. Biſect AS in G, and erect the perpendicular GH equal to 3M, and a circle deſcribed about the centre H with the interval HS, will cut the parabola in the place P required. For letting fall PO
