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

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32
Mathematical Principles
Book I.

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 impreſſes forces and takes off velocities proportional to the times; and the times of aſcending to the greateſt heights are as the velocities to be taken off, and thoſe 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 ariſing from its projection as compounded with the motion ariſing from its gravity.

Figure 3

As if the body A by its motion of projection alone (Fig. 3.) could deſcribe in a given time the right line AB, and with its motion of falling alone could deſcribe in the ſame 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 deſcribes, will be a parabola, to which the right line AB will be a tangent in A; and whoſe ordinate BD will be as the ſquare of the line AB. On the ſame Laws and Corollaries depend thoſe things which have been demonſtrated concerning the times of the vibration of pendulums, and are confirmed by the daily experiments of pendulum clocks. By the ſame, together with the third Law, Sir Chriſt. Wren, Dr. Wallis, and Mr. Huygens, the greateſt geometers of our times, did ſeverally determine the rules of the Congreſs and Reflexion of hard bodies, and much about the ſame time communicated their diſcoveries to the Royal Society, exactly agreeing among themſelves as to thoſe rules. Dr. Wallis, indeed, was ſomething more early in the publication; then followed Sir Chriſtopher Wren, and, laſtly, Mr. Huygens. But Sir Chriſtopher Wren confirmed the truth of

truth