Final answer:
Galileo revolutionized the field of astronomy by using mathematics, making groundbreaking observations with the telescope, and emphasizing observation as the determinant of truth.
Step-by-step explanation:
Galileo revolutionized the field of astronomy in several ways. First, he used mathematics to analyze and understand the physical space and motion of celestial bodies. By applying mathematical analysis, Galileo was able to connect real-world observations to the ideal mathematical world. Second, Galileo's use of the telescope allowed him to make groundbreaking observations, such as discovering moons orbiting Jupiter and the phases of Venus. These observations challenged traditional beliefs and paved the way for a new understanding of the universe. Finally, Galileo's emphasis on observation as the determinant of truth revolutionized the scientific method and laid the foundation for future scientific discoveries.