## History and applications

### Kinematics before Newton

There is no surviving evidence that Archimedes, or the other truly great Greek mathematicians Euclid and Apollonius, studied kinematics. But so much of Archimedes' work has been lost that it is hard to know.

The representation of quantities by lengths and areas has a long history. In the 14th century, Nicholas Oresme represented time and velocity by lengths. He invented a type of coordinate geometry before Descartes.

The need for mathematical descriptions of velocity contributed to the development of the concept of the derivative. In the 14th century, scholastic philosophers at Merton College, Oxford, studied motion with constant acceleration and deduced what is now known as the Merton rule:

An object with constant acceleration travels the same distance as it would have if it had constant velocity equal to the average of its initial and final velocities.

This rule corresponds to the second equation of motion from the section Constant acceleration.

In the 17th century, Galileo Galilei (1564–1642) and others discovered that, in a void, all falling objects have the same constant acceleration, and so their motion may be determined by using the Merton rule. Galileo may well best be remembered for his battle with the Catholic Church over his support for Copernicus' heliocentric model of the solar system, but perhaps he deserves to be remembered as the founder of modern physics. As early as 1604, Galileo discovered that falling bodies are uniformly accelerated. He then worked out a number of mathematical consequences of this fact, some of which could be confirmed by experiment. His work was held back by primitive equipment — for example, there were no stop watches available. Part of his work concerned projectiles, and he was aware that their paths are parabolic.

Next page - History and applications - Sir Isaac Newton (1642–1727)