Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/76

32 proportional times are as the velocities and the times conjunctly; that is, in a duplicate ratio of the times. And when a body is thrown upwards, its uniform gravity imprees forces and takes off velocities proportional to the times; and the times of acending to the greatet heights are as the velocities to be taken off, and thoe heights are as the velocities and the times conjunctly, or in the duplicate ratio of the velocities. And if a body be projected in any direction, the motion ariing from its projection as compounded with the motion ariing from its gravity. As if the body A by its motion of projection alone (Fig. 3.) could decribe in a given time the right line AB, and with its motion of falling alone could decribe in the ame time the altitude AC; compleat the parallelogram ABDC, and the body by that compounded motion will at the end of the time be found in the place D; and the curve line AED, which that body decribes, will be a parabola, to which the right line AB will be a tangent in A; and whoe ordinate BD will be as the quare of the line AB. On the ame Laws and Corollaries depend thoe things which have been demontrated concerning the times of the vibration of pendulums, and are confirmed by the daily experiments of pendulum clocks. By the ame, together with the third Law, Sir ''Chrit. Wren, Dr. Wallis, and Mr. Huygens, the greatet geometers of our times, did everally determine the rules of the Congres and Reflexion of hard bodies, and much about the ame time communicated their dicoveries to the Royal Society'', exactly agreeing among themelves as to thoe rules. Dr. Wallis, indeed, was omething more early in the publication; then followed Sir Chritopher Wren, and, latly, Mr. Huygens. But Sir Chritopher Wren confirmed the truth of Rh