How Kepler derived that T^2 is proportional to r^3

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Kepler's third law states that the square of the orbital period (T) of a planet is directly proportional to the cube of the semi-major axis (r) of its orbit. Kepler derived this relationship through empirical observations of planetary motions rather than from gravitational theory. His findings were later supported by Newton's law of universal gravitation, which provided a theoretical framework that explained Kepler's empirical laws.

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How did Kepler exactly prove that the period squared is proportional to the radius cubed? If he didn't prove it. Then how is it proven?
 
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Mapes said:
http://en.wikipedia.org/wiki/Kepler's_laws_of_planetary_motion#Deriving_Kepler.27s_third_law"

Kepler did not derive any of his laws from the law of gravity.
He found it by experiment, using the observation data of the planetary motions to find the relative distances and the periods of the orbital motions and then looking for a relationship between these quantities.
Newton's law came later and it was supported by the fact that it can explain the laws that Kepler found by "experiment".
 
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