Eudoxus of Cnidus (c.390-c.340 BCE) was the world’s greatest mathematician before Archimedes. He made significant contributions to astronomy and philosophy. History remembers him as the person who proposed a Method of Exhaustion. This project explores Eudoxus’ formulation and application of the Method of Exhaustion, which is used to find the area and volume of a shape by inscribing polygons inside of it, with an increasing number of sides. This method was deemed a precursor to integral calculus and set a foundation for many concepts that were used by later mathematicians. Also, this study analyzes Eudoxus’ invention in comparison to the modern limit theory. Owing to that, emphasized Eudoxus’ mathematical thought and his influence on both ancient and modern mathematics.