either Time , Height , or Velocity being assign'd, one may readily find the other two. From them likewise is the Doctrine of Projects deducible, assuming the two following Axioms ; viz. That a Body set a moving, will move on continually in a right Line with an equable Motion , unless some other Force or Impediment intervene, whereby it is accelerated, or retarded, or deflected.
Secondly, That a Body being agitated by two Motions at a time, does by their compounded Forces pass through the same Points, as it would do, were the two Motions divided and acted successively. As for Instance, Suppose a Body moved in the Line GF, (Fig. 1. Tab. 5.) from G to R, and there stopping, by another Impulse, suppose it moved in a Space of Time equal to the former, from R towards K, to V. I say, the Body shall pass through the Point to V, though these two several Forces acted both in the same time.
Prop. V. The Motion of all Projects is in the Curve of a Parabola : Let the Line GRF (in Fig. 1.) be the Line in which the Project is directed, and in which by the first Axiom it would move equal Spaces in equal Times , were it not deflected downwards by the Force of Gravity . Let GB be the Horizontal Line , and GC a Perpendicular thereto. Then the Line GRF being divided into equal Parts, answering to equal Spaces of Time , let the Descents of the Project be laid down in Lines parallel to GC, proportioned as the Squares of the Lines GS, GR, GL, GF, or as the Squares of the Times , from S to T, from R to V, from L to X, and from F to B, and draw the Lines TH, VD, XY, BC parallel to GF; I say, the Points T, V, X, B, are Points in the Curve described by the Project , and that that Curve