COR. 6. If the periodic times are in the sesquiplicate ratio of the radii
The sesquiplicate is the square root of the cube, in this case, the Orbital Period is proportional to the square root of the distance cubed. Kepler's third law states that :
D^3 𝞪 T^2
Therefore,
T 𝞪 √ D^3
He then inputs this into a simple speed = distance over time formula :
V = D / T
V= D / √ D^3
V = √ 1 / D
Then, combining the centripetal force formula, V^2 / R, with the above, he arrives at the groundbreaking force equals the inverse of the distance squared formula :
the centripetal forces will be in the duplicate ratio of the radii inversely :
At this point, Newton stops to give credit to other english physicists for the famous formula :
as Sir Christopher Wren, Dr. Hooke, and Dr. Halley have severally observedBut he has omitted the origin of his starting point, Johannes Kepler, a giant whose shoulders Newton was standing on more than anyone else.
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