Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/213



How the motions are to be found in given orbits.

To find at any aigned 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 uppoe 4ASxM equal to the parabolic area to be cut off APS, which either was decribed by the radius SP, ince the bodies departure from the vertex, or is to be decribed 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. Biect AS in G, and erect the perpendicular GH equal to 3M, and a circle decribed about the centre H with the interval HS, will cut the parabola in the place P required. For letting fall PO