Democritus, Empedocles, and other Pre-Socratics developed proto-scientific theories unable to make precise, testable predictions. Things changed in the 17th century.
The Scientific Revolution began in 1543 with the publication of Copernicus’ heliocentric theory of the solar system.
Copernicus’s system postulated circular orbits for the planets. Deferents and epicycles were used to explain their retrograde motion.
Beginning in the 17th century, scientific theories were formulated mathematically, yielding testable predictions.
Johannes Kepler’s Three Laws of Planetary Motion (1609-1618)
Ellipses: the orbit of each planet is an ellipse with the Sun at one focus.
Equal Areas: an imaginary line drawn from a planet to the Sun sweeps out equal areas in equal times.
Harmony: (the orbital period of a planet)2 is directly proportional to (the average distance of the planet to the sun)3.
Galileo’s Laws of Falling Bodies and Projectiles (1609)
Falling Bodies: the (distance a body falls) is directly proportional to (elapsed time)2
Projectile Motion: the trajectory of a projectile is a parabola
Isaac Newton’s Theory of Gravitation (1687)
Using the magic of differential equations (F=MA), Newton’s theory predicted, second to second, the motion of falling bodies and the orbits of the planets
Galileo in 1623:
“The laws of Nature are written in the language of mathematics.”
A Philosopher's View 