How did Renaissance thinkers, such as Galileo Galilei, best contribute to the progression of science?

Galileo relied completely on what today is understood as the scientific method direct observation and experimentation rather than the Bible or received tradition in his study of astronomy.

Explanation:

Galileo was the towering scientist of his age, much as Einstein was in the twentieth century. If, as we should, we associate the Renaissance with the beginning of the movement from the centrality of faith to the centrality of reason, he is the exemplar of reason for his period.

He developed the telescope, he was able to study the movement of the planets, discovering the four largest moons of Jupiter and determining that Aristotelean cosmology (a received tradition) was in error, causing a huge stir in the scientific community.

Galileo also studied velocity, dropping balls of different weights (again using the scientific method of direct observation) from the top of the leaning tower of Pisa to time how quickly they fell. He demolished Aristotle's contention that objects of different weights.