Final answer:
Galileo Galilei used empirical observation and mathematics to validate his theories about the universe. His use of the telescope to observe celestial bodies like Jupiter's moons and the phases of Venus provided evidence for the heliocentric model and laid the groundwork for modern astronomy.
Step-by-step explanation:
Galileo Galilei, a key figure in the scientific revolution, used empirical methods to prove his theories. He was particularly adept at using mathematics to understand the physical space and motion of celestial bodies. Observation and experimentation were at the core of his methodology. He challenged prevailing views by making careful observations through his telescope, leading to discoveries like the moons of Jupiter and the phases of Venus, which provided crucial support for the heliocentric theory initially proposed by Copernicus.
Galileo’s commitment to observation over 'logical' argument led to significant conflict with religious authorities. His findings were in direct contradiction to ancient beliefs and religious teachings of the time, resulting in a trial by the Inquisition and subsequent house arrest. However, Galileo’s astronomical work, including observations of countless stars and the Milky Way as a multitude of individual stars, was later validated by others and accepted into scientific and even religious understanding.