256 THE MATHEMATICAL PRINCIPLES ~ [BOOK II I a parabola in a non-resisting medium. For the latus rectum of this parabola, at the very DV2 beginning of the motion, is -y-', andVris tGT DR x T* -~JT- or £^T — . But a right line, which, if drawn, would touch the hyperbola GTS in K G, is parallel to DK, and therefore T* is CKX DR c QBx DC ^ , and N is — ~pp • Ahd thereDC DR2 X CK x CP fore Vr is equal to 2DC2 X QlT~; *^at *S (Because D^ anth the velocity of the body and the resistance of the medium in each of the places r. For the ratio of CP X AC to DP X DA being given, there is given both the resistance of the medium at the beginning of the motion and the latus rectum of the parabola ; and thence the velocity at the be ginning of the motion is given also. Then from the length of the tangent