He carried two different sized stones which dropped on floor at the same time.
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1. Floor should be replaced with ground. Ground means the surface of the earth.
2. The stones were dropped from the top of the tower by Galileo and (they/the stones) reached the ground at the same time.
It was the spirit, which (=spirit?) Galileo testified our judgement and theories through nature directly, that led to ...
If you replace "which" with "spirit" in the clause, does it sound right?