beginning of the motion is given alſo. Then from the length of the tangent rL, there is given both the velocity proportional to it. and the reſiſtance proportional to the velocity in any place r.
Cor. 6. But ſince the length 2DP is to the latus rectum of the parabola as the gravity to the reſiſtance in D; and, from the velocity augmented, the reſiſtance is augmented in the ſame ratio, but the latus rectum of the parabola is augmented in the duplicate of that ratio; it is plain that the length 2DP is augmented in that ſimple ratio only; and is therefore always proportional to the velocity; nor will it be augmented or diminiſhed by the change of the angle CDP, unleſs the velocity be alſo changed.
Cor. 7. Hence appears the method of determining the curve DraF, nearly, from the phænomena, and thence collecting the reſiſtance and velocity with which the body is projected. Let two ſimilar and equal bodies be projected with the ſame velocity, from the place D, in different angles CDP , CDp; and let the places F, f, where they fall upon the horizontal plane DC; be known. Then taking any length for DP or Dp, ſuppoſe the reſiſtance in D to be to the gravity in any ratio whatſoever, and let that ratio be expounded by any length SM. Then by computation, from that aſſumed length DP, find the lengths DF, Df ; and from the ratio , found by calculation, ſubduct the ſame ratio as found by experiment; and let the difference be expounded by the perpendicular MN. Repeat the ſame a ſecond and a third time, by aſſuming always a new ratio SM of the reſiſtance to the gravity, and collecting a new difference MN. Draw the affirmative differences on one ſide of the right line SM and the negative on the other ſide; and through the points N, N, N draw a regular curve N N N, cutting
