Greek rationalism deals with trying to understand the world using logic and observation. While non-Greek contemporaries had similar ideas, Greek philosophy formed the basis for Western rationalism. Greek rationalist philosophy is still taught.
Socrates, Aristotle, Plato and other Greek philosophers wrote and talked extensively about how to understand the world. While there were some similarities between most Greek philosophers, many took different approaches. Aristotle took a particularly materialist view of the world, while Plato believed reality to be a reflection of a greater truth. While Plato remains influential, the work of those who wrote about Aristotle helped craft modern rationalism.
Perhaps the most important Greek philosopher for modern rationalism was Democritus. He took a skeptical view of many issues, but he also questioned the reliability of human senses, which modern science has shown to be flawed. The Greeks did not develop rigorous scientific testing procedures, but the work of Democritus would encourage later philosophers to try to divorce the observer from the experiment as much as possible.
Greek rationalism was later refined by philosophers in Arab-controlled lands while Europe was in the Middle Ages. As Europe emerged and entered the Renaissance period, the annotated Arabic translations of ancient Greek works became popular topics of study, and the Greek and Arabic texts formed the basis for modern rationalism.