How did Galileo Galilei use mathematics in studying nature?

Galileo Galilei transformed natural philosophy by insisting that the book of nature is written in the language of mathematics. This shift moved the study of nature away from purely qualitative, verbal accounts toward a mathematical framework where experimentation served as a primary method for discovery.1

His mathematical approach led to fundamental breakthroughs in the science of motion, including:

• The Law of Falling Bodies: Galileo determined that the distance a body falls is proportional to the square of the elapsed time.2
• Projectile Motion: He discovered that the trajectory of a projectile follows a parabola.12
• Inertia: He formulated a concept of circular inertia that challenged existing Aristotelian physics.1

Beyond theoretical physics, Galileo applied mathematics to practical inventions, such as designing a hydrostatic balance for weighing small quantities and creating a proportional compass, or sector, for use in fields like fortification. His work established a rigorous, quantitative foundation for modern science.21