"If the earth attracts the moon, why does not the moon fall to the earth? A glance at the accompanying figure will help to answer this question. We must remember that the moon is not stationary, but travelling at tremendous speed—so much so, that it circles the entire earth every month. Now if the earth were absent the path of the moon would be a straight line, say MB, If, however, the earth exerts attraction, the moon would be pulled inward. Instead of following the line MB it would follow the curved path MB. And again, the moon having arrived at B, is prevented from following the line B'C, but rather B'C. So that the path instead of being a straight line tends to become curved. From Kepler's researches the probabilities were that this curve would assume the shape of an ellipse rather than a circle. ...Kepler's observations of the movements of the planets around the sun was of inestimable value; for from these Newton deduced the hypothesis that attraction varies inversely as the square of the distance. Making use of this hypothesis, Newton calculated what the attractive power possessed by the earth must be in order that the moon may continue in its path. He next compared this force with the force exerted by the earth in pulling the apple to the ground, and found the forces to be identical! "I compared," he writes, "the force necessary to keep the moon in her orb with the force of gravity at the surface of the earth, and found them answer pretty nearly!" One and the same force pulls the moon and pulls the apple—the force of gravity. Further, the hypothesis that the force of gravity varies inversely as the square of the distance had now received experimental confirmation."
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Benjamin Harrow, From Newton to Einstein: Changing Conceptions of the Universe (1920)
https://en.wikiquote.org/wiki/Ellipse
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Ellipse
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