- 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

- Johannes Kepler’s
- Galileo in 1623:
- “
*The laws of Nature are written in the language of mathematics.*”

- “
- A scientific theory is an axiom system:
- designed to explain certain kinds of phenomena
- defined by its postulates
- supported or disproved by its predictions