Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 2.djvu/68

 54 The refiiiattce of phærical bodies in fluids aries partly from the tenacity, 'partly from the attrition, and partly from the denity o the medium. And that part: of the reitance, which aries from the denity of the fluid, is, as I (aid, in a duplicate ratio of the velocity, the other part, which aries from the, tenacity of the fluid, is uniform, or as the moment of the time: and therefore we might now proceed to the motion of bodies, which are refifted partly by an uniform force, or in the ratio of the moments of the time, and partly in the duplicate ratio of the velocity. But it is fuiiicienl: to have cleared the way to this peculation in the 8th and 9th Prop. foregoing, and their Corollaries. For in thoe Propoitions, iniiead of the uniform reitance made to an acending body ariing from its gravity, one may fubfiitute the uniform reitance which aries from the tenacity of the medium, when the body moves by its"z/is infra alone; and when the body acends in a right line, add this uniform reitance to the force of gravity, and ubduct it when the body decends in a right line. One might alo go on to the motion of bodies which are refified in part uniformly, in part in the ratio of the velocity, and in part in the duplicate ratio of the ame velocity. And I have openeda way to this in the 13th and 14th Prop. foregoing, in which the uniform reitance ariing from the tenacit of the medium, may be fubfiituted for the force ofygravity, or be compounded with it as before. But I. hafien to other things.,

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