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Michael Johnathan McDonald, April & May 2006, U.C. Berkeley, History 181A., Spring 2006.
Newton's calculation with Kepler's laws, R. Hook asks Newton, ' What happens if a ball is dropped in a crevice?'
Newton said, as shown below, and this shows diurnal motion of the Earth. Hook reportedly said that is would make a smaller circle.
|Laws of centers and inertia.
Δ is assumed not a strait line. Galileo hated the idea of strait lines ( See Day One Dialogue).
Here are my notes.
Newton here is utilizing into the geometry Kepler's equal area law, however he will drop time to make this an entirely geometricy because area equals time.
The attraction of interacting bodies. Assume the distance is a small constant, treated as small quantities. Kepler's first law here with inertia exists with the centrality of the acceleration.
|Orbital Dynamics. Galileo's free fall law is used by Newton all the time.|
force law for the ellipse goes directly as the distance
between the interacting bodies.
Book two of the Principia wiped out Descartes system.
|In Book three, the universal principle of gravity shows bodies tending toward each other. All gravity is lending to everything else at the same time.|
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