the right line SMMM in X, and SX will be the true ratio of the reſiſtance to the gravity, which was to be found. From this ratio the length DF is to be collected by calculation; and a length, which is to the aſſumed length DP, as the length DF known by experiment to the length DF juſt now found, will be the true length DP. This being known, you will have both the curve line DraF which the body deſcribes, and alſo the velocity and reſiſtance of the body tn each place.
Scholium.
But yet that the reſiſtance of bodies is in the ratio of the velocity, is more a mathematical hypotheſis than a phyſical one. In mediums void of all tenacity. the reſiſtances made to bodies are in the duplicate ratio of the velocities. For by the action of a ſwifter body, a greater motion, in proportion to a greater velocity, is communicated to the ſame quantity of the medium, in a leſs time; and in an equal time, by reaſon of a greater quantity of the diſturbed medium, a motion is communicated in the duplicate ratio greater; and the reſiſtance (by Law 2 and 3.) is as the motion communicated. Let us therefore ſee what motions ariſe from this law of reſiſtance.
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