Rationalists argued that starting with intuitively-understood basic principles, like axioms of geometry, one could deductively derive what was true. Descartes, with his mathematical background, was naturally drawn toward this method, and famously claimed to derive his own existence from pure reason (cogito, ergo sum). On the heels of his work came continental philosophers such as Spinoza and Leibniz who sought to enlarge and refine the fundamental theory of rationalism.
Immanuel Kant started as a rationalist, but after being exposed to David Hume's works which "awoke [him] from [his] dogmatic slumbers", Kant arguably synthesized the rationalist and empiricist traditions.
See also: Rationalist movement